Yeah BRP isnt too fun for combat. After learning more about Genesys and deciding its not meant for Supers and high levels powered monsters, I think we are going to use the FASERIP system for our Arkham game.

But Im still interested in seeing what you do with this.

Great stuff. I will try to have my group play a Cthulhu game, but more oriented towards the FFG LCG Arkham Horror Card Game.

First step, working on those Archetypes: Guardian, Seeker, Mystic, Rogue and Survivor.

One unusual feature of your interesting system involves recovering Sanity in excess of maximum as a result of Keeper award or improving a skill to 4+. As an investigator's max sanity drops, it will become easier to regain enough to exceed that amount over time. That would mean recovering from Madness more often as the game goes on - which may be what you want, although I don't recall this happening in BRP, and you've obviously thought hard about emulating that system. If you like the idea of "curing" madness this way, you could make it harder by adding setback dice = Mythos skill on those rolls. Or just make it impossible to cure madness without Psychotherapy.

Another issue - if Advantages give you Sanity back, it's possible to gain sanity after rolling. My character will be looking for corpses all day

What is the down side for trying self-help? Can your Sanity get worse if you roll poorly?

You may want to explain what a Reality check is for, since it appears in CoC but not Genesys.

The more I look at the question of sanity, the better this answer looks: use the fear check rule from the back of the book, and add a setback die for each rank of Cthulhu Mythos skill the character has. If the source of the check relates to the Mythos, change one or more difficulty dice to challenge dice.

I think it's important to preserve Genesys' ability to narrate a roll, rather than to provide a concrete result for every conceivable outcome. Call of Cthulhu is unique in that Sanity rolls get harder to make over time, while 99% of games make skill rolls easier.