What's that? It's what I use instead of the weak jump overcall. The CJO is the equivalent of a Raptor 1NT-overcall; the jump to 2H/S shows 4-card in the overcalled major and 5+ cards in an unbid minor and about 11-15 hcp. This treatment lets you get this awkward hand off your chest in one bid and is more difficult to cope with for opps than the Raptor 1NT. We've been using it for over 10 years now, btw (Lindkvist-Fredin among others)
But, this doesn't solve the problem after a 1S-opening with 4H & longer minor. So what to do? Revert to Raptor here? No, you can still use the 'non-jump canapé overcall' of 2H and use 1NT to show a heart overcall! By interchanging the meaning you get to keep the meaning of 2M consistent AND get your heart suit in at a more convenient level.
The idea of using (1S) - 1NT as showing 5+ H is something I came up with -95/96. This convention lets us get hearts in the picture cheaper and provides room to play in 1NT/2m if doubled or misfit. With constructive values, we can start to explore strain and level with more accuracy. The biggest downside is that it may wrong-side an occasional 3NT-contract.
So what about (1H) - 1NT? I use it to show both minor suits (54+). Why? Because more points gets exchanged on 2-suiters than 1-suiters and by pinpointing both minors when we are potentially outranked by the majors gives us a chance to evaluate the fit and bump the level. Downside is wrongside (NT). Another plus is that you also make it a bit more difficult for the opponents to find spades (no neg X).
After (1C/D), I favor a natural 1NT-overcall. If you can't stand that, you can use 1NT as 54+ in M's (and let the cue-bid be specific 2-suiter with highest and lowest).
All this may take a while to digest, but I recommend it and it is battle-tested against the best. My current partnership is so new that we haven't gotten around to these 'extra' treatments yet (just the CJO).