Does your Omega actually shift POI? Some don't when removed. One easy, no-modification solution is a torque wrench so the screws go in the same each time.
Just like the ACP conversion, it's not that there is something inherently wrong with the gun....the problem is 777, not the gun. ANY gun can be monkeyed with and improved, and the Omega is no exception. There is an endless supply of after-market improvements for the Remington 700, a top-quality factory rifle. I decided to monkey with mine and see how far I could take it, that's why I installed pillars and bedded it. The result was very convenient disassembly and greater accuracy, but it wasn't absolutely necessary as a torque wrench would have done it too.
Modified to say that you shouldn't have to disassemble an Omega for every cleaning anyways.