Steel-Dwass has very little power with small group sizes. If you have group sizes around n=15 or greater, it will probably be a decent option. Years ago, I was looking for a Tukey HSD analysis with an unequal variances correction and came across Games-Howell, which is not available in JMP. I added it to the JMP Wish List, and is one of the most up-voted proposals on there right now. In the last year, I created an add-in to do Games-Howell on a single X and Y which you can find here:
https://community.jmp.com/t5/JMP-Add-Ins/Games-Howell-Test-Tukey-HSD-with-Welch-s-correction-for-Une...
I know you are wanting to do the multiple comparisons relative to a control, which I don't have an exact solution for, but if you are willing to do a Tukey-style analysis and just look at which levels are not connected to your control, you may get what you need from that add-in.
-- Cameron Willden