I'm not seeing you running on uneven ground, avoiding bush's while the heart is pumping hard and seeing anything being reloaded while moving. Maybe a shot shell I am guessing. Not quite in the same league as moving from or to engage DG at close range.

I have loaded SXS shotguns on the move and it is not that easy when on uneven ground or in bush and keeping the barrels in a safe direction. Can be done but takes time, relatively speaking. It is far easier and quicker to change a magazine on a bolt gun or stick an extra round in a fixed mag on some bolt guns. ie on a CZ 550 but not say a Rem 700.