I downloaded the track twice, but the file seems to be corrupt. I see you doing the pivot, but you're about 2,000 feet in the air. Also, there's no text or voice.
I tried doing your suggestion (pushing down on the stick) in the P-40, and I after fiddling with the brakes and rudder I eventually got it to work. I still can't do it consistently, however, which makes me suspect that my pedals are broken. Well, I mean even more broken than I know.
Right now, only one toe pedal works. So I have that bound to universal brake. Then I have my differential brakes bound to the Z and X keys. The only way I was able to pivot on a wheel in the P-40 was to give full down elevator trim, then give full left rudder, hold the Z key, then depress my working toe brake. When I did those steps out of order, it didn't work. Something's funny and I can't tell if it's the game, my settings, or my pedals.