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I went instead with the classic hp and strength stats. Later, when outlining the battle routine, it became apparent that I would also need a speed stat to mimic the turn-based style of Final Fantasy

It's interesting that he went for speed. I'd probably go for a physical vs. magical split, to throw players on situational pinches - like, you built your char to be strong on a certain attack (physical or special = magical), but the monster is strong against that attack and weak to the other. Then set up the HP to a fixed amount (like 100), and increase/decrease damage based on the defences.

The result would be Atk/Def/MgA/MgD, so a bit more complex than his HP/Atk/Def.