If you have a cascading relief and the valve is conventional it may be that the CDTP (cold diff test pressure) is being shown instead of the set pressure on the P&IDs. I've seen this mistake in the past. 

Does the thermal PSV go to atmosphere or into another line with another thermal PSV? 

Example: if your PSV relieved into a line with another PSV set t 50psig,then the CDTP of the PSV should be set 50psig less than the required set pressure, but P&ID should show the set pressure i.e. CDTP + the 50psig. 

If its a proportional relief valve like a Swagelok PSV typically used on chemical injection tubing follow the curves supplied by vendor. These valves do not fully open at 10% overpressure so while the rated capacity is high the capacity at the allowable accumulation may be far less. See link . https://www.swagelok...n/MS-01-141.pdf. 

Typically for pilot PSV the backpressure correction factor will be less than 1 at Total backpressures greater than ~ 40-50% so it is not ok to assume 1. Best thing to do is get the vendor catalogue for the PSV and look for the back pressure correction curve. Or email the vendor and ask for it.

With regards to your Total back pressure this is superimposed + built-up back pressure which is what you have done.

Also,

Make sure your flow is still critical at 65% back pressure. It may be sub-critical. If so the subcritical sizing equations should be used. Alternatively API does give another backpressure correction curve which can be used with the critical flow sizing equations.