I’ve been towing with the 68RFE for years. What people don't realize is that these transmissions depend heavily on line pressure to keep the clutches from burning. How I keep mine alive: I NEVER tow in 6th gear on grades. I always lock out 6th, and sometimes 5th, to keep the trans from "hunting" for gears.
That mushy feeling is the computer trying to smooth out the shift to be "comfortable," but comfort kills these gearboxes under load. Get a custom trans tune (like RevMax or similar) that increases the line pressure. It will make the shifts feel much firmer, which sounds worse but is actually much better for the life of the clutches.