I, too, have issues with heaps, leading me to believe there could be some bad translation from windows system calls to wine system calls, involving some sort of heap transversal. Looking at some of the errors, maybe there are memory OOB problems happening, but I'm not sure. WTB better third party support.
I'm not getting any heap "errors" from Wine, but from STO itself. I'm getting D3D unrecognised formats and some Shader debugging from Wine, and then the Cryptic error launcher thing.
I'll point out too, that last line is due to a typo in my .asoundrc, which shows whenever a new app is starting. I haven't fixed the typo, as it gives a good indicator of when wine is spawning new processes The D3D unrecognised format errors and Shader stuff all come basically before the Cryptic logo shows up, so I don't think they're the cause either.
Also, running "GameClient.exe" in Cryptic Studios/Star Trek Online/Live/ gives the console output, same as adding the "-console" option in Options. Just a quicker way to test things, without having to log in. Don't know if the whole "not logging in" may add to the troubles though.
Scrolled through the console log, saw some errors about PhysX.dll missing, so I installed PhysX via winetricks, now it's giving an "error" that CUDA support isn't found. I'm not sure what to make of it, but I doubt CUDA is a "requirement".