This linear axis 30-80 cm long and 3-5 cm wide may imply a very long and narrow body tetrapod, as known from the fossil record (Cretaceous and early Tertiary casts of the gut only).
You are asking what tetrapod has an intestine consisting of tightly coiled loops, but non-spiral. This description is not entirely clear to me. Could you please specify it or -if possible- provide a photo/draw?
The spiral valve is found in various vertebrate taxa, but never in tetrapods and teleost fish (Gilmore, 1992; Hunt et al., 1994; Bajdek, 2013).
My best guess is that you are asking about so-called "sideritic coprolites" most famous from the Upper Cretaceous (Madagascar, Saskatchewan) and the Miocene (Washington), but known even from the Permian, which were interpreted as cololites (intestinal casts) by Seilacher et al. (2001). If they are cololites indeed, they must have belonged to a variety of vertebrate taxa. It's hard to say much from your description. Regarding the position of the intestine and the body shape of the animal, you should consider carefully taphonomic factors.
I think someone could help you more if you specify your question...
Literature
Bajdek, P., 2013. Coprolite of a durophagous carnivore from the Upper Cretaceous Godula Beds, Outer Western Carpathians, Poland. Geological Quarterly 57(2): 361–364.
Gilmore, B., 1992. Scroll coprolites from the Silurian of Ireland and the feeding of early vertebrates. Palaeontology 35(2): 319–333.
Hunt, A.P., Chin, K., Lockley, M.G., 1994. The paleobiology of vertebrate coprolites. In: Donovan, S.K. (Ed.), The Paleobiology of Trace Fossils. John Wiley, London, pp. 221–240.
Seilacher, A., Marshall, C., Skinner, H.C.W., and Tsuihiji, T. 2001. A fresh look at sideritic „coprolites”. Paleobiology 27(1): 7–13.
I am the original discover of the voluminous southern Saskatchewan deposit of tens of thousands of Late Cetaceous coprolites. I spent about 10 years excavating the deposit in the late 1970s, and wrote 2 papers on the deposit:
Paul L. Broughton, Frank Simpson and Sidney H. Whitaker, 1978, Late Cretaceous coprolites from western Canada, Palaeontology, volume 21, part 2, pages 443-453.
Paul L. Broughton, 1981, Casts of vertebrate internal organs from the Upper Cretaceous of western Canada, Journal of Geology, volume 89, number 6, pages 741-749.
However, I have recently started to take up the dispute as to whether these specimens are organic or inorganic in origin. Attached is a specimen, part of one, from the Washington Miocene deposit. It, exactly like the Cretaceous Saskatchewan material, consists of tightly sinuous back and forth loops along a linear axis, that can extend for tens of cms (not spiral valve). For various reasons I do believe that the morphology can remain linear during burial and therefore it begs the question: Is there a modern animal (or even a Tertiary or Cretaceous) with a linear to curvilinear axial gut? So far as I know, all larger animals that would have a gut approaching multi-meters (see my Journal of Geology article) would presumably pack a body cavity with intestines that are not linearly arranged. Yet, the very tight sinuous packing along such an axis does imply a very elongated "snake-like" very digestive system. What kind of animal do we know of with that? Is there any modern analogue?
I know your 1978 Palaeontology paper since I was a kid and I just requested the 1981 Journal of Geology paper which I haven't read yet; very sorry for not having noticed it's you who asked this question.
I would be very glad to see a new paper discussing the origin of these structures, but strictly morphological criteria may be not too convincing. Personally, I have only examined four limonitic specimens from Madagascar under a stereoscope microscope, which were given to me as "coprolites". I'm not convinced that any of the few specimens I got is a coprolite, but in theory they might be cololites; one posssibly revealed some longitudinal striation (as mentioned on some specimens from the Saskatchewan in your Palaeontology paper). A few months ago, I published a short popular science book (in the Polish language) were I also summarized some ideas from the Seilacher's paper. I think it would be however nice to find any new lines of evidence.
Your idea is interesting, but to me it sounds as rather hard to prove convincingly that the linear morphology of the structures implies a given kind of source animal. Moreover, I deliberately mentioned that such specimens are known even from the Permian deposits, which might suggest they are of quite diversified vertebrate taxa. You might be instead interested in searching for some kind of geochemical evidence or remains in the specimens which would help to determine their affinity or at least to prove they are fossils indeed, although I know that not much have been preserved in these strongy altered diagenetically specimens.
By the way, I would like to show you in private something from the Miocene of Poland, I believe comparable to specimens from the Saskatchewan and Washington.
Thank you for the pix. These are morphologically identical to the Saskatchewan, North Dakota and Washington material---and a vey commonplace classic
coprolitic form known from many places in the world. No doubt about it in my opinion--but not potentially fossil intestine material. The potential for intestinal material based on morphology is more likely when: (1) the shape has sufficient interwoven twists that it somewhat has a pretzel-like continuity (2) there is a very long continuous looping back and forth (not spiral valve which is another matter) such that it is inconceivable that it could be expelled from the body in a single piece, such a meter or two long. The Miocene specimen pix I originally attached is a small segment of such material, and therefore in my opinion intestinal. Meter or longer specimens, so far as I know, are only known from two localities in the world, in the US and Canada such as my original deposit in southern Saskatchewan (Journal of Geology article). However, I know of no modern animal vertebrate descendent that has a linear extended gut consisting of loops along a linear axis. That begs the question of taphonomy. I do not believe that a multi-linear meter long gut would be preserved within burial unless it was originally that shape: unbroken or and undeformed in cross-section--especially when there are no signs of compaction.
Thank you for the comments on the specimens from the Miocene of Poland!
I fully agree with you that if the sideritic/limonitic specimens are bromalites indeed (and are not e.g. inogranic in origin), the largest and most complex ones are cololites rather than coprolites.
However, meanwhile you suggest that the smaller ones (as those from Poland) are coprolites, I'm personally some more inclined to say that at least a significant part of them are cololites too.
The potential for intestinal material based on morphology is more likely when: (1) the shape has sufficient interwoven twists that it somewhat has a pretzel-like continuity (2) there is a very long continuous looping back and forth (not spiral valve which is another matter) such that it is inconceivable that it could be expelled from the body in a single piece, such a meter or two long.
Your argument is that the specimens are too simple morphologically to prove they are cololites, but:
1) Although this may be a good point, it's obviously not an evidence that they must be coprolites - at best it means that we don't really know what kind of bromalites they are. On one hand, one might expect that coprolites should be more common (since feces are left in great numbers during the whole life of their producer in contrast to cololites potentially left only after the animal's death), but on the other hand e.g. Seilacher et al. (2001) suggest that unexpelled fecal material might have a higher fossilization potential than fecal matter expelled to the environment.
2) I can see no significant difference between them and the larger specimens - they just look as small fragments of those large "cololites". If so, it seems some more parsimonious to assume they are cololites too (untill you find a good evidence they are coprolites), especially because:
3) In fact, the small specimens reveal some characteristics of cololites rather than coprolites. I attach a photo of a specimen from the Cretaceous of Madagascar. Compare it with the Fig. 3 in Seilacher el al. (2001):
"Figure 3. More-slender variants from the Washington occurrence consist of segments whose pinched ends are closely apposed. This is the result of peristaltic waves that transported the contents along the dynamically meandering gut. Since the contracted sections were empty, they are not represented in the intestinal cast."
This seems to refer perfectly also to the morphology of the specimens from both the Cretaceous of Madagascar and the Miocene of Poland (and as it seems also to specimens from the North Dakota, Saskatchewan and China). For example, at the attached picture the central part of the specimen is clearly composed of two parallel segments (this is very characteristic to sideritic/limonitic "coprolites") as described by Seilacher et al. (2001). Because this is to me the most convincing argument, I'm especially interested in your explanation...