Actually the Trade Machine says this wouldn't work - Knicks would be giving us $33,542,393 and we would only be giving them $28,555,855.
According to the TM we would need to add an additional $852,440 (at least) to make it work.
If we throw in Bogans than that makes it a perfect match. Probably makes it more tempting for the Knicks as well...they get back $17M in expiring contracts (Hump + Bogans) and only have to take on $17M in long term contracts (Wallace + Bass). Bass' deal is only for two years, so that's no worse off than the Amare/Andrea deals. That means the only part they will get stuck with for longer is the extra year at $10M for Wallace. That's basically a $17M saving for them come the end of this season, giving them the flexibility to makes some deals to improve the team and convince Carmello to return.
In addition to that they get four extra players on their roster. The combination of Bass+Hump is probably more productive for them than Amare+Bargnani (if they want to make a Playoff run) and they could probably use defensive energy-guys like Wallace and Bogans on the bench.
They would need to clear two roster spots to make it happen though (as this would put them at 17 players under contract). I'd be happy enough to take Kenyon Martin and Toure Murray back...we could either keep them or buy them out for instant cap space.
So the end result would look something like this:
Knicks send:
------------
Amare Stoudemire
Andre Bargnani
Kenon Martin
Toure' Murray
Celtics send:
-------------
Kris Humphreys
Gerald Wallace
Brandon Bass
Keith Bogans
How is that?