My go to source for peroxide decomposition kinetics and relief design is a paper by Michael Grolmes of Centaurus Technology: "Pressure Relief Requirements for Organic Peroxides and Other Related Compounds" from the 1998 International Symposium on Runaway Reactions, Pressure Relief Design, and...
If you prefer a hardcopy and your responsibilities require a thorough understanding and quick reference, you might consider the Steam Tables texts (SI & English) by Keenan & Keyes. Should be able to get used copies pretty cheap.
Equation 35 in ISO 4126-10 includes the backpressure as part of the mideal term as pseat from equation 32. It is not as explicitly stated as in the API documents. From the variable definitions following equation 34:
"pseat is the pressure in the seat cross-section of the safety valve, expressed...
Soft seats are tight to 95% of set when >100 psig. Not as good as a pilot (~98%), but better than a metal seat and a decent option if your company avoids pilots (some operators just don't like them for various reasons). If the improved seat tightness eliminates the simmering then you're going to...
What is the PRV protecting? Just the pump casing or the downstream equipment and piping too?
Consider setting it higher, if possible, based on the design pressure of the protected equipment. A pilot operated PRV would be a good solution as previously suggested. If a pilot is undesirable, would...
Your PHA will tell you when a PRV is required from a process safety perspective. Equipment design standard (ASME, API, etc.) will indicate when a PRV is required for code requirements. Your local oversight and inspectors (OSHA/NB) will tell you when a PRV is required (or missing) for compliance.