What kind of data have you got? You gave up quite readily on OLS methods, which are actually pretty robust in many situations where they are considered taboo, such as liker-type items and non-normal variables.

First, I agree with Ronán that OLS methods are far more robust than many people think.

Second, I had never heard of the Steel-Dwass test.  But a quick Google search brought me to the article at the first link below.  From p. 572 in that article:

"This Steel-Dwass method, which possesses several desirable properties (Morley, 1982), is based on pairwise rankings. It was generalized for the case of unequal sample sizes by Critchlow and Fligner (1991)." (emphasis added)

Critchlow, D. E. and Fligner, M. A., 1991: On distribution-free multiple comparisons in the oneway analysis of variance. Communications in Statistics – Theory and Methods 20, 127–139.  (see second link below)

HTH.

http://onlinelibrary.wiley.com/doi/10.1002/1521-4036%28200109%2943:5%3C571::AID-BIMJ571%3E3.0.CO;2-N/abstract

http://www.tandfonline.com/doi/abs/10.1080/03610929108830487

Reading the SAS STAT User Guide (online) can help. It depends on if this test has migrated over to SAS. My paper copy from 1988 discusses each test and ends with some overall suggestions for which one is better gives specific circumstances. Of course my copy doesn't include this test. With a date of 1991, the generalized version should be in JMP, but it would be really nice if the JMP user manual would confirm this.

There are also a large number of articles on the use of multiple comparison procedures that can be found on the internet. I googled "SAS multiple comparison" and got this (amongst many others): http://www2.sas.com/proceedings/sugi24/Stats/p264-24.pdf.

If you go to a test like a randomization test you could also try and show that the variances are different even if the means are not.

Also try log transforming the data. This does not always help, but it is a good strategy to try. There may be other transformations that might be more appropriate depending on your data.

I typically spend as much time analyzing the data as I do collecting it. If the main goal is to get through the analysis as quickly as possible, then Tukey's HSD is a good choice. It may still be the best choice even if you try a number of other options. You just won't know until you try. The other risk is that you are standing by your poster (or at a meeting), and someone asks why didn't you use the Kruskal-Wallis test, or any of the other dozen or so possible methods? Looking blankly is not a good strategy. It is more interesting if you can say something like "I looked at Dunn's test, Ryan-Einot-Gabriel-Walsh multiple range test, Wilcoxon, and a randomization approach, but in the end I chose Tukey's HSD because there was no qualitative difference in the outcome of any of these and Tukey's HSD is more commonly used." You have shown that you have thought about the problem, and put some effort into your data analysis.