What's causing the bulging are the plastic cases. Plastic is more elastic than brass and the brass head bulges out and stays while the plastic goes back to it;s normal diminutions.
I use 444's because I use them for heavy 410 loads in my derringer and buckshot in my BFR. I also shoot plastic and brass 410 shells in the BFR. I'd use brass 410 cases (Which would fireform) in the 45/70 except the extractor rides over the rim. The 444's extract fine and fireform to size.
The choke does add a lot of versatility to the gun and this Handi, will do a lot of service on my tractor, ATV and truck. I take my BFR on them now but I'd rather use a $200.00 Handi as a beater, than a custom tuned $1000.00 BFR.