With respect to the majority of other proteins the quantitative determination of collagen (COL) is a task not to be taken for granted. Direct colorimetric or ELISA assays can be carried out only on fully soluble COL corresponding  either to the natural precursor (usually present in tiny amounts) of the physiological insoluble COL or to soluble degradation products obtained artificially (e.g. pepsin “solubilized”). On the other hand soluble COL might undergo aggregation/gelation and so on while conversely pepsin usually do not “solubilize” completely the insoluble COL. Therefore looking for a reliable quantitative determination, total COL hydrolysis to single amino acids followed by OH-Pro quantification would appear as the master way even if slightly demanding.

If you have access to a NanoDrop, you could measure it that way (280nm wavelength I believe).  Just complete a curve with some BSA in water, and compare it to that.

As collagens mostly consist of glycin, proline and lysine (P and K later being hydroxylated), I doubt that direct photometry will give useful results. I'd try Biuret reaction first, preferably with a calibration curve derived from a weighted collagen sample.

Copper based reagent (e.g. BCA) or amino reactive dyes (eg Dansyl chloride) actually should work.

If nothing else helps (i.e. in worst case), I'd resort to hydrolyzing my samples and standards at elevated temperatures with 6M HCl to single amino acids and then quantify.

The method of choice depends on a) the levels of collagen present, b) the levels of contaminating protein, (the latter are likely to strongly interfere with Bradford assays as collagen has relatively low aromatic and basic amino acid content), c) components likely to interfere with various assays e.g. detergents. You mention a thick liquid so the following should be a safe bet you can probably afford to dilute your material in the appropriate buffer. Bacterial collagenases cleave collagen into very short peptides. The latter can be detected via a variety of sensitive assays for primary amines. Simply estimate these before and after digestion. Use pure collagen as a standard substrate and avoid any primary amines in the buffers. 

Dear Rachael, if the protein content in your sample is within 20 -100 mg/ml, the biuret reaction can be used to quantify your protein (Gornal et al, 1949). You should ensure that your protein sample is fully dissolved. From your description of the isolate, a really thick precipitate may be quite rich in protein. But ensure it is sufficiently dissolved when using any method of quantification.

Dear Rachel,  considering that type I-III collagen is composed by 13-14 % of OH-Pro, the main way to quantify collagen is the determination of hydroxyproline after 18 hour hydrolysis in 6 N HCl at 108 °C and HCl removal. It might appear challenging however at the end you overcome any kind of problem (solubility, preparation etc) thus obtaining highly reliable results.  Colorimetric kits are readily available from major companies.

Dear Rachel,  The Sircol assay is a colorimetric assay developed specifically for triple-helical collagen.  My group has also had success developing our own ELISA assays for lower concentrations of collagen.

With respect to the majority of other proteins the quantitative determination of collagen (COL) is a task not to be taken for granted. Direct colorimetric or ELISA assays can be carried out only on fully soluble COL corresponding  either to the natural precursor (usually present in tiny amounts) of the physiological insoluble COL or to soluble degradation products obtained artificially (e.g. pepsin “solubilized”). On the other hand soluble COL might undergo aggregation/gelation and so on while conversely pepsin usually do not “solubilize” completely the insoluble COL. Therefore looking for a reliable quantitative determination, total COL hydrolysis to single amino acids followed by OH-Pro quantification would appear as the master way even if slightly demanding.