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Seconding the Drury recommendation -- you need to have a way to slow partner down when you open these hands (and seconding everyone else that you need to open these hands at matchpoints).
I don't think 1H is indefensible here as an opening. Slam is not out of the picture, e.g. is 50-50 if partner has Ace of hearts and Ace of clubs. I would probably open 4H though because it's matchpoints and you're vulnerable, which means missing a thin slam isn't a catastrophe (whereas letting the opponents find a spade fit might be).
I also would not double. In addition to the concern you raised about partner bidding too high, this hand has poor defensive strength and partner might erroneously penalize a "sacrifice."
Just a quick additional answer -- a hand plays very quickly in bridge; rarely more than 5 minutes after the auction. In a typical evening session with 28 boards, you'll be dummy roughly 7 times, and it's a nice time to relax the brain a bit.
@GendoIkari the linked questions asks if you can move into the safety zone (you can't -- that's not backwards); this asks if you can move to just outside it (you can)
+1. clarification in case OP is relatively new to bridge: by "fast rebid" you mean, "at the next round of bidding." of course the tempo, slow or fast, of the rebid itself, cannot legally be taken into account by partner!