Most users just use MME with BBWin, I remember there was a wineasio.
I haven't got a Linux running at the moment, I did have Ubuntu Studio when I was trying it all.
Reaper worked very well under wine and the native Linux version should be able to use Open SGU in Reaper if it's set to anything but wma like wav or flac or mp3 etc... the BB VST should work using wav how it is now but could be made to work the same way as Open SGU in Reaper where you can choose any Reaper compatible format to use.
I don't know if Gordon tried the Open SGU in Reaper with Linux Reaper ?