"Question: do you trust the gun bearer enough to leave the DR he is carrying loaded? Or do you leave it unloaded?"

Carry it unloaded IMHO.

How long does it take to grab a DR, drop 2 rounds in and fire ?

Not that long to someone who is practiced but the more important question IMHO is will you need to bring the OTHER DR to bear that quickly - I think maybe you should have time to swap guns.