So once again thanks to all the information provided in this thread and all the links from this thread I've compiled my Tribble spreadsheet to the point that I'm only missing a few remaining combos.
I've determined there are 1,716 known possible breeding combos. This includes all 66 food types and 26 Tribble types (which of course includes the mysterious unverified 26th Tribble). Based on everything I've verified myself, seen reported by others or at least "predicted" by others there are only 36 combos I have no clear clue about. They are as follows:
Hopefully these will be bred soon enough. I didn't bother to get a Rivera preorder Tribble because I expect based on how Cryptic historically handles these things that it'll be available via the C-store sooner or later so I can't check many of these myself but I'll be trying for the ones I can do.
Once these are done (and reported) all combos will be available to everyone at that point.
Based on a bit more analysis the following combo should be true: Rivera + Klingon Octopus = Stacy
Obviously that needs to be verified but that only leaves 35 combos to go...
Eh, technically money's not an issue for me either. But then again I've already spent like $400 on this game for several other preorders and the lifetime deal so I couldn't quite bring myself to spend like another $50 just for a Tribble. Who knew I'd actually become interested in all this Tribble breeding stuff lol.