Hello Shortround6,
I will blame YOU for this little continuation.

I remembered reading your comment above about large fuel tanks and greater fuel load but could not find it in the data table I use the most for a reference. The two versions of the Yak-9 were close enough in specs to be twins off the same production line so there had to be a reason why 2748 Yak-9T were built as opposed to only 53 Yak-9K.
The data table in "Yakovlev's Piston Engine Fighters" suggests that the two aircraft were near twins as far as performance as well, but not all sites agree, so there had to be something else going on.
Here is what I believe was the "Rest of the Story":
The first version of the Yak-9K didn't just swap the big cannon for a bigger cannon.
It also added about 150 KG of extra fuel in the wings.
The larger cannon bore didn't change the weight of the gun, but it did make the BORE of the gun larger of course and even though the barrel wall was made to be very thin where it went through the propeller reduction gear shaft, it still left much less clearance than the 37 mm barrel did.
Recoil was many times higher, but the muzzle brake was fairly efficient and brought the recoil energy down to BELOW that of the NS-37 cannon.
This was still quite severe recoil and was still causing fatigue damage to the airframe just as it was for the NS-37.
My Note:
I suspect that total energy was lower, but the impulse and peak force was still higher. The vibrations from firing also probably brought the cannon barrel into contact with parts of the propeller reduction gear because the clearance was on the order of fractions of a millimeter.
The performance with the extra fuel tanks was so poor that they were removed and the weight became comparable to the Yak-9T.
Even without the extra fuel, the pilots felt that these aircraft were too heavy to be ideal for fighting other fighters and should work in combination with Yak-3 or Yak-9U.
The effectiveness of the NS-45 in aerial combat was actually better than the NS-37. On average, 10 shots were fired per kill as compared to about 30 shots per kill for the 37 mm.
The problem though was that the NS-45 also had very poor reliability and that was the real reason that the aircraft never went into production.
- Ivan.