I only had an omega p01 for a short time and did not study the inner workings, so unfortunately I have no good advice.
I would give Cajun Gun Works a call, as he advised me on refitting the detent in the 75 compact to give it a more positive click, but decided not to do it.
I can relate though:
I considered my CZ75 compact and cz 85 compact thumb safety’s to be so astonishingly weak and mushy I manually decocked it, pointed into a planter. They did not feel safe for carry and I tried a few holsters and still found the sometimes disengaged except in a kydex holster that covered the safety completely.
I on the 75 compact, I actually used a 1911 plunger tube spring, cut 1/3 off the length, and was able to cram it into the CZ75 compact behind the sear cage and had around 3k trouble free rounds before selling it. The 85 I never carried and sold.