The '36 is an enclosed torque tube driveline and rear end, so it has to go when the T5 is swapped in. And if I am not mistaken, you cannot even change gear ratios in these old differentials.
Right.
You unbolt the third member and torque tube assembly and remove it all as one big piece from the axle housing, and bolt in an open drive third member from a 55-62 truck in its place, then fab or modify a driveshaft to replace the torque tube. Replace or otherwise immobilize the pivoting spring perches, and you're set. That's what I did on my 50, and that's what my friend did on his 29 using a 39 truck housing, which brings me back to wondering how similar the 36 truck and 39 truck housings are, and if it could be an option for you.
There are/have been 3.38 gears available for them, but in my personal experience, as-is the 3.90 works very well with the tire size, overdrive ratio, and inline 6 power band.