I think checking the injectors and new fuel are the only potentially logical things left to check. If you mixed fresh fuel with old fuel, it could start well for a month. It could also age prematurely because it's been innoculated with stale fuel. Stale fuel can make starting difficult in marginal conditions. The injectors being opened up exposes them to contamination, old fuel could gunk them up, etc.
The compression does seem to be the main problem, these are secondary, but if it runs acceptably, then I'd run it at least to find out what the machine needs in addition to rings/pistons/sleeves. You may never need to rebuild it if it runs good enough.
It runs fine, so the metering valve is functioning eventually, when you shut it off, push the shut off rod back in after the engine is off, then it will be in position to start and won't stick off. And run fresh fuel.