I have a 350 in a 58. I use a TH350 and it works well with 3.08 gears. I assume you plan to change the rear end. My 58 had 3.90 gears original. Running a 400 transmision and the old rear end causes the gears to be turning much faster and may fail due to high revs. Lots of options for rear ends that have higher gears.
Why would using a TH400 make the rearend fail? It has the same final drive as a TH350 and even the stock transmission used in most old GM trucks, 1:1. Even running an overdrive gear won't make a difference, as the idea behind an overdriv isn't higher speeds, but reduced engine rpm at any given speed. Besides, those old Eaton HO33s are pretty tough. I've ran mine at 75 mph + in overdrive, no issues at all.