Ok, reviewed the film and compared it with the default auto climb speed.
In TJ film it took the Yak-3 about 2:35 minutes to go from 750ft to 9.9k (measured from the moment it started to roll). All while staying very close to 100mph indicated
At default climb speed (auto climb), it took about 2:43 minutes for the same altitude difference, at climb speeds between 130 to 160 mph.
And just for the nitpicking record, in neither way the Yak-3 goes from SL to 10K in under 2.5 minutes, and the 109K (WEP) is still faster. But of course this isn't meant as a comment on the validity of the Yak-3 low speed climb capability.