I am a saxophone/clarinet / flute player, but my girlfriend is a bassoonist and whenver I pick hers up just for fun I can see that with some work producing a good sound and controlling the pitch would be less of an issue than the fact that the fingerings are totally screwed up.
Question: If you've already got got saxophone, clarinet and oboe (for which I have huge admiration for you) chops, why not add flute to your arsenal as it is much more called for on doubling gigs?
Reeds seem to be a big issue too fro bassoon. Finding reliable ones that don't play too sharp or learning how to make them well is a cause for much frustration.