The frame is unbalanced. Let's look at the numbers for two frames.
Frame 1:
Allies: 66 pilots got 49 kills. Objects destroyed: 34
Axis: 63 pilots got 92 kills. Objects destroyed: 45
Frame 2:
Allies: 63 pilots got 56 kills. Objects destroyed: 2
Axis: 60 pilots got 88 kills. Objects destroyed: 32
In both frames, the Axis completely destroyed their targets.
Compare weapons loadout and performance on the opposing aircraft. "It's the pilot, not the plane" is not always the answer.
Let's look at your numbers compared to just the success of the LA-5's in these frames.
In Frame 1, the Allies had 18 LA's. The managed only 10 kills in total, 9 of which were in the first sortie.
In Frame 2, the Allies only used 10 of the 16 LA's they were allowed to use. Those 10 pilots only achieved 7 kills in total, 2 of which were in the first sortie.
I'm highlighting the first sortie numbers because both frames were decided before the 2nd hour planes were enabled. Looking at the total kills does not paint the true picture.
So before you complain about the lack of firepower in the Yak-9 or C.205, you need to figure out why your side is failing to find success with your best overall plane.
The LA is a close match to both 109G-2 and 190A-5 at 20K. Below 12K it is completely dominant over the G-2 and A-5. The gun pack of the LA-5 packs a punch but has poor ballistics and firing rate, but the plane's performance should mean that you are able to close in on an enemy to a place where those issues are mitigated. Aggressively flown LA's are nearly impossible to shake in a either a 109G-2 or 190A-5. If the CiC fails to put the LA's in a place to be flown aggressively, and with a strength to do so, that's his fault. Frame 1, they were in a bad place. Frame 2, they were under strength.
I'm not saying that the Yak-9T pilots aren't in a difficult position, but it's really hard to quantify the disparity when the LA's are performing so poorly. If the kill totals showed that the Yaks were struggling while the LA's were scoring kills in bunches, I'd give credence to your thesis. But that is not the case.
Regarding the Yak and C.205,
Adding the C.205 mitigates the Yak's speed disadvantage at altitude. This should have allowed the Allies CiC to use the Yaks better to its strengths. It's a very good fighter at lower altitudes and the 37mm cannon is a monster against large targets. For the 109's to match that firepower, it requires using the performance sapping 20mm gondolas. Yaks and C.2's should be successful against 109's outfitted with them, and LA's will dominate them at every altitude.
Since the Axis actually lost the war, I do have the right to complain.
You really need to know when to play the "Historical Accuracy" card better.
First, there is no "Better Yak" as in January 1943. The Yak-9, M with 20mm cannon or T with the 37mm, is the best there was at the time - and January 1943 might be too early for either. The vast majority of Yaks at this time were Yak-1s and Yak-7's. The Yak-9U did not enter service for another year and a half. Your suggestion for a "better Yak" is as unfounded as the Axis would be asking for 109G-14's or 190A-8's.
Second, the MiG-3, which the C.205 represents, had a total production run of 3172 airframes, only 52 of which had 20mm cannons. That's .016% of the total built. All other MiG-3's had a combination of 7.62mm and 12.7mm machine guns, just like the C.205 minus the cannons. Furthermore, the final 30 cannon armed MiG's were built in April 1942 and it's anyone's guess which units received them or how many survived the 8 months of combat leading up to the battle of Velikiye Luki. The point being, the chances of there being even one cannon armed MiG-3 at Velikiye Luki in January 1943 is essentially zero.
Third, The Allies have the LA-5FN which is a type not introduced for another 6 months. The units in January had standard LA-5's with worse performance, higher weight, and worse visibility. Because AH only has the FN, The Allies have a better fighter than they should. By the same margin, the AH 190A-5 is worse than the 190A-3's and A-4's actually used at this battle. The performance differences within plane types (LA-5 to LA-5FN or 190A-4 to 190A-5) are not significant, but the performance gap between sides would be wider if we had the correct models. Would not not make a huge difference, but since you want to play the "Historical Accuracy" card, here we are.
The fact is, in January 1943, the Soviet air force struggled to compete on an equal footing against the Luftwaffe because they failed to employ their assets properly. Seems that this FSO is not far from history in this regard.
Here's the upshot, the Allies are at a natural disadvantage in fighters, but it's no worse than the Axis typically faces when the Allies have Jugs, Ponies, or Corsairs. Your side is doing poorly mostly because your pilots and planners are failing to use your assets to their strengths.