Framing question - potential sagging soffit

Trying to save ceiling height in my basement remodel - wife says: (can't you get it higher?)...... So... below is my soffit drawing. I've got monster HVAC ductwork to get around. Built the soffit essentially with 2X2's but the more I look at it - the more I worry about the ceiling sagging after I put on drywall. I've got 3 1/2 ft. spans essentially with no way to support them more than I've got. If I go back and put 2X4's on edge, I lose another couple of inches of ceiling. Thoughts? Will the soffit hold - or do I sacrifice the ceiling (which would still be in code - but lower than wife wants it).

if i got you right you have 2x2 spaning 3'6".
doesnt sound bad. if you are worried, after inspection, put long fine threaded drywall screws thru 2x2 into trunk line

You could always strap the 2x2's in the opposite direction and that would pull everything together and you would only lose another 3/4".

Thanks guys... I've got screws in everything to avoid nail slippage - and braced to the upper floor joists as much as possible. I'm going with it as is I guess...... for lack of a better plan....