The Broad’s DepMap project was the most serious effort in this area that I’m aware of. They focused on cancer cell lines but also included normal cells as controls. My understanding is that the pan-essential genes are typically required in both cancer and normal cells making them difficult to target. It’s possible that focusing on functional features rather than specific genes could get around this but is more difficult to operationalize. In some ways, chemotherapy already does this by targeting rapidly dividing cells. An alternative approach is to focus on pan-cancer immunotherapy which could leverage the specificity already present in the patients immune system. The use of endogenous IgG accumulation could be an interesting approach along these lines.
If the mutations are shared with both your parents and neither of them share the phenotype, it seems unlikely these are major loss of function mutations, however, it would be interesting to know if anyone else on the side of your family with the frame shift shares this trait with you. If you are at all cost sensitive and have some basic lab proficiency, you could easily spot check the relevant region without long read genome sequencing. Just isolate genomic DNA and PCR up the region. Nanopore sequencing (like plasmidsaurus) can sequence the PCR bands for ~15$ would let you see if the mutations are coming from the frame shift copy or not.