I used to do a little mx work on the
TPE-331.
(turbo-prop engine?) Mostly as installed on Metros and Jetstream 31s but some others too.
Yes, rotating the prop by hand shortly after shutdown is done to minimize the effect of shaft bow by ventilating the engine with cooler air. As I recall, the primary effect of shaft bow is excessive abradeable seal wear on the next start. And IIRC from the Garrett TPE-331 line mx school in PHX 22 years ago, resonance is indeed the concern WRT the restricted RPM range. I've seen similar restrictions on a couple of piston engined propeller driven planes as well.
Very efficient engines. Especially when measuring efficiency on a noise per pound of fuel basis! (well... at ground idle anyway... They quiet right down when you take 'em off the start locks and push the torque up a bit.)