News from Jeff Armstrong:
I'll have to look at the 190 ROMs, but I'm pretty sure they're unlabeled. In the meantime, I was able to transplant the Turbow-286 card and ROM into another Rainbow and managed to get the system to boot (still having serious issues, though).
I've attached the two ROM dumps. I'm pretty sure that ROM1 is the stock 100B ROM, although my system has a ClikClok installed in between ROM1 and the board (I doubt that'd make a difference in the ROM dump). ROM0 is labeled: "TBSS 1.3" on line 1 and "3ED4" on line two (a checksum perhaps?).
I do have hi-res versions of the Turbow pictures somewhere. I'll have to look, but they should be accessible via the gallery I host. The chips aren't overly interesting, except that there does appear to be a GAL, which will make emulating it a pain. I remember reading that one of the chips, a 286-to-8088 adapter chip, was quite exotic at the time.
I'll let you know when I find the pictures and check for Rainbow 190 ROM labels.