Most battery mfg's publish data and OCV tables for their batteries like the one above. You didn't mention your OCV or temperature so can not say your SOC. Cranking 9.0 vdc indicates starter, wiring or battery not optimum.
It seems like your initial issue of pump re-priming in rapid succession has resolved since your r-r the ignition switch. If it re-occurs then post your observations and any diagnostic steps you've taken. If this were my mc then I would not be replacing HES at this time.