I too would love an answer to this question. Don't want to give up the perfection of my 7800 hood ergonomics. But need a new front der, and would like to "upgrade" weight and shifting, if possible.

7800, 7900 and 9000 all have different cable actuation ratios for the FD. They will all "work", to some degree, with each other, but it depends on what your definition of what working means. If you want optimal shifting for a given set of STI levers, you'll need to go with the corresponding FD.

7900 FD with 7800 STI and the levers won't pull enough cable to shift the FD properly

7900 STI with 7800 FD - the 7900 levers have no inner ring trim stop since they were designed to use the 7900 FD which has a wider cage that the 7800 FD. You'll get a lot of chain rub and not be able to adequately get rid of it.

9000 FD is too new and too unavailable to know, but that huge lever arm has got to require a markedly different cable pull then either 7800 or 7900 FDs.

7900 front derailleur with 7800 shifters and 7900 crank will not move the FD enough. If as above, but with 7800 crank, it'll be fine.
9000 may or may not work with current shifters. 9000 has a long arm, yes, but the cable passes very close to the arm's pivot point, making the effective arm length effectively very, very short. That's how shimano managed to make 9000 have such a light fd shift action.

For those that might like to know, I have just mounted a FD-9000 together with a Campa Record 11s group, and so far it works pretty good!
It takes 3 clicks to shift up, and the first click I can use for trim while on small ring.
On big chainring, there is only a bit of rub on derailleur when chain is all crossed up - a gear I would never use anyway.

It is only tested in workstand so far, so can't yet say for sure if it works 100% on the road. Will let you know when it gets a bit warmer outside