Question on 350 Turbo to 400 Turbo swap

[phil g]

I have a 77 short wheel base 2wd truck.
I want to replace the 350 turbo trans with a 400 turbo.
I know that I will have to change cross member location, mount, yoke,
maybe modify the driveshaft length and change the kick down setup - my question is will the 400 fit without interference with the floor pan. Two of the shops in the region that do lots of square body vehicles claim that the 400 is physically too large to fit a "low hump" floor board and I will have to modify the floor to get the larger transmission to fit. Not a big deal, I just don't want to cut up my floor. I think that they are full of it and the 400 will fit without problems.
I want a 400 because I want this to be a backup tow vehicle for a small tandem trailer.
I would like feedback from someone that has actually done this swap and not just read about it on the internet. Thanks for your input