I need some help with the following:

I'm trying to put a 40t outer chainring on a 44t-32t-22t 3x9 XT crank. However this doesn't work because the front derailleur plate is hitting the middle chainring when shifting to the outer chainring. Thus, the tooth difference between the outer and middle chainring is too small.

Does anybody know a good way to solve this? Is there any front derailleur that will accept this smaller difference?

Just set the front derailleur so it will clear the middle ring?!
(ie. move the derailleur up about 5-10mm.)

You will have more than the normal 2-3mm of clearance between the big ring and the outer plate of the front derailleur (something more like 7-13mm) but as long as you set your outer limit screw well it will shift well enough and you shouldn't have any major problems with overshifting.

I don't think you'll find any derailleur that you handle such a small difference in chainrings any better.

Good luck.
Let us know how it turns out.