Thing is, south has a pretty good hand, and he can massively discount his heart losers when he's counting them. I'd bid 1S-then-4H. It's pretty damn close to 4H though. I'd bid 4H without the CA, but I don't want to oversell this hand.
Re: 1S v 1N. The benefit of 1S is that if partner has Hx or something, he can value it highly, which is what you want. But if you have a (5-4+) spade fit, you're basically never playing in hearts now, and now you're vulnerable to an opening heart ruff if they can find it. On frequency, he won't have a fit too often, so this is the route I choose. I can definitely understand the value of bidding 1N and being able to unambiguously show hearts, but you don't get any of the side features of your hand across. I am sure you'll find people doing both.
Side comment: I think denying outside 2nd rd controls is insane. IMO you shouldn't be jumping to 4H without shortness. And I think xxx / xxxxx / Kxxx / x is a pretty normal jump to 4H, and you don't want to be taking the same approach (1N-4H) with this hand and the one in OP. Also I don't understand your comment at all -- you say that 4H denies an outside 1st/2nd rd control but you'd bid over 1H-4H...
If we bid 1S... I disagree that partner will bid 4S here. He's got 4 losers and can definitely do something more (4D seems about right), after which I'll just cue 5C. Partner will show the void with 5D, and we'll just bid 5S and he just has to raise with his hand (or bid 6H in which case we'll play 6S). Yes this is probably vulnerable to an opening ruff and a bad spade layout. This is a bad layout for our approach here.
If we took the 1N route, we hit the friggin jackpot when partner reverses into spades (which is not GF for me). Then 3H by us IS GF and sets trump. Now partner bids 3N, a serious spade cue (DC -- I recommend that in ser/non situations in hearts, you invert 3S/3N), and we bid 4C. Now he'll ERKC in diamonds as long as LHO didn't dbl 4C for the lead
, and we'll play 6H.