I think that ACKS' main strength is bringing robust high-level/domain play rules to the OSR ecosystem. It means that you can use bits and pieces of ACKS with your favorite OSR system, so you have use of ACKS even if your main ruleset is, say, Labyrinth Lord. This creates a wide market for ACKS beyond those interested in ACKS per se (such as myself). Thus, compatibility with other OSR rulesets is a selling point and you should be careful not to distance ACKS too much from the OSR ecosystem in order to maintain that market segment.
So, I think that keeping the current core magic system is a necessity. However, transplanting other HFH rules, such as the healing and Fate Point rules, would be excellent and will not harm compatibility too much.
Also, D20-type attack throws (roll high w/ bonus/penalty vs. a fixed DC) will work well; Sword & Wizardry: White Box has these, as does BFRPG. These are easy to explain to newcomers and are, as I noted above, compatible with several OSR games. I'd use the same basic system for saving throws as well.
That said, a stand-alone "high level play and economic rebalancing" book for D&D 5E would be awesome. There are already some products along these lines IIRC, but ACKS has the best economics and high-level play in the market.