Medium and hard throw in new kinds of operations, but how hard a problem is for me at least seems to mostly scale with the number of digits I have to juggle, not the operation "complexity".

E.g. if I'm at 14, an "easy" multiply "by itself" forces me to multiply long-form (I don't even have 4 x 14 in my mental LUT... so 140 + "uh... 56 plus..."). On the other hand, again starting at 14, a "hard" multiply by 4/7 instead is trivially 8 (mentally rewriting to (14/7)*4)

It is. I failed a few easier (ran out of time, or got wrong results), but complete hard ones without any issues.

Also, easy has stuff like "7x12", which is not-so-easy (you only usually memorize multiplication tables up to 10x10).

Hard, however, has things like "54/9", which is trivial and I could have done being 10 years old in an instant.