It's been a few years since I was flying a turbo 210 (or a C340, essentially the same engine x2), but, offhand, 120lbs/hr seems too lean for climb, though maybe not for 30". In general, you're right, the mixture should not have to be adjusted during climb. Temperature-wise, I do recall having to have the mechanics tweak fuel flow with seasonal temperature change, as in, winter setting would not be just right once warmer summer temps came on, and vice-versa.
I believe the entire setup procedure is in this (very extensive!) service directive from Continental, SID 97-3G. A google search will turn up pdf files for this bulletin.
Not sure any of this will help, as I said, it's been a few years for me.