Better can be an annoyingly ambiguous word, particularly when referring to recovery from illness. "I'm better" can mean either "I've recovered now", or "I am better than I was before, but not fully recovered yet".
Which is strange. We don't use "I'm best" in the first instance, so need a modifier, which is the kind of thing the question wants.
Natural to me, is much better, which I'd take to mean "fully recovered"; though it still doesn't go all the way. Is there a residual superstition about not claiming to be fully well in case fortune takes its revenge on such gross assumption? Or is it an unvoiced acknowledgement that we can never be "fully well" anyway?
This cautious approach is also seen in the modifier for a degree of recovery: I'm feeling better, which seems to acknowledge that we frail humans might consider something to be so and so, but the gods of reality know better. Much better. Most better.
Incidentally, the proscription against a "double" comparative or superlative (more better; most better) ignores the earlier usage in English, in which "more" and "most" act as intensifiers, adding the emphasis that the question asks for. It's a construction used many times by some of the best known writers of the past ( shakespeareswords.com )
"In profane authors there are also many instances of the use of the
double superlative. Sir Thomas More used the expression, 'most
basest'; Ben Jonson that of, 'most ancientest'; John Lilly (of the
time of Queen Elizabeth) that of, 'most brightest'; and Shakespeare,
'most boldest, most unkindest, most heaviest.'" ("On the Language of
Uneducated People," The Saturday Magazine, August 24, 1844) - about education
I like this robust forcefulness.