Stealer of Souls - Potential New Keyword Fix?

I've been playing a mix of Battlegrounds and Ladder recently, and whilst playing Battlegrounds, I came across the Prophet of the Boar. Now the interesting thing about this card is the Once per Turn being keyworded on the card, despite it being only used on this particular card.

With Stealer of Souls being as troublesome as it has been, could it be changed to the following instead?

This would allow the effect to still go off this turn, either via tap or the first card drawn off of Backfire for instance and if it lives until future turns, the effect can be done again. However, these massively reduces the "pop-off" potential for the card. I don't know if this is the correct change for the card, but seeing as it utilises something that is already found within the game, I thought this would make for a good discussion.

once per turn is used a lot in yugioh,  the game is too fast for me now but i always loved this kind of design, i would like this change.

A possibly more elegant solution would be to change it to say "Battlecry: draw a card. It costs health instead of mana".

As an elegant and tbh more 'typical' change, the battlecry change is pretty good. However, the once per turn mechanic still allows this to activate across multiple turns if it survives, just with a much lower scope than it currently has. I'd also like to see if 'Once per Turn' could work as an adjustment to other pop-off cards like this one. I'm unsure which ones I'd target, but I'm sure it's a mechanic that could be used, even for new cards to replace old ones.

For instance, this could be a replacement for Gadgetzan Auctioneer whilst that rotates to wild format, if the auctioneer is ever deemed too powerful. Probably won't be any time soon but this is just a further adaptation of the idea. It may be too weak, but again this is just a very basic and easy example of something that could happen.