Pete,
I wonder if you have considered moving the HVAC air handler to the other end of the basement bathroom since the stairs in that location have been eliminated.
It looks like it would centralize the unit better. I don't know how they had planned running the hot and cold air trunk lines taking into consideration the two wooden cross beams I added in "brown"
I would think running them as I have depicted cold=blue, hot=red would make a little sense. That way they could be hung from the bottom of the floor joist, leaving the little gap required at the top and not stick down much, if any, more than the beams. The red hot trunk may need to be sized down as it goes toward the perimeter of her house.
The hot laterals to each room would then fit between the joists. I would want a cold air return inside the master bedroom in case your mom or whoever in the future likes to sleep with the door closed.
I'm not a heating engineer so your company will, of course, design for the best flow..let's hope.

, along with not messing up more basement space than absolutely necessary.
I'm not an architect, either, but it appears to me from the drawings you posted that the perimeter studs of the house are 2 x 6?
Ron