[@ClocktowerEchos]If i make it 1944-45 my technology would undergo a drastic change.
I deliberately chose a close date so we don't need to rewrite our sheets.
By 1944 I'd be parading around with jet fighters and first gen guided weapons among others.
Anyways, I can't see why you need late WW2 era for heavy AA guns. 
Also I thought it was the point that the Black Turtle is just a myth or a rare and prohibitedly expensive tank. Say a true super prototype.
My heavy tanks would be owned by a smug noble's Aramegir and they would be a wholly independent unit with rather small numbers.
Your Black Turtle could be a "hero tank" of sorts. Say, the Lancelot of your nation. Except it's a tank.
As for semi-auto rifles and machineguns, nothing stops you from having them. 1942/43 development means they can be pretty much standard.

As for AA effectiveness, only one-third of the V1s were shot down by the combined efforts of Britain's AA and fighter interception. You'd have far less of these and potentially more frequent and more accurate bombings. I am not saying you'll be annihilated or anything close. With the limit of 10,000 I can't even have one of my supreme airships which is actually fine because that's the air equivalent of navy support. My flying bombs also have weaknesses other than radio jamming but I leave that for you to find out.