TT Air pressure

First off there's no ST tires in that size that uses 32 psi. The lowest is 50 psi.
All trailer rims are rated the same per size and all ST trailer tires have the same load ratings per size. Doesn't matter what brand.
14-5.5 rims are rated for 2200 lbs.
205/75/14 LRD are rated at 2040 lbs at 65 psi.
If you have newer style aluminum rims, that is you're not looking to put tires on a 20 year old TT then the above ratings would apply to you.

Agree with above - max sidewall PSI

As long as the Rims can handle the pressure won't hurt to run at higher psi. This will not increase your load carrying capacity because of axle ratings. The Rims should be stamped on the inside with max psi rating.

The only question is can the rims handle 65psi, hopefully whoever mounted them would have noticed if they couldn't but I'd double check and then air them up to Max cold.

One of the reasons for up grading the load range from "C" to D"" like you did is so you can inflate to a higher pressure....thus gaining more payload and reserve capacity..
Pump them up to the sidewall max pressure..They will run cooler and have less chance of failure..

On trailers inflate to the max as listed on the sidewall.