Don't move him to a new place. Feed him in the tank he's comfortable in. All that work on not stressing and acclimating him to it goes out the window if you move him to a new place.

Also think about this: People say feeding in the tub/tank means they think every time you reach for them that you're food, so you're more likely to get bitten, right? If that applies then:
A-) Going in to take them out and put them in a new tub means they expect food so they'll bite (false as is the original premise)
and
b-) The actually true one? MOving a snake while it's 'in feeding mode' or right after feeding is riskier than feeding them to start with. It also increases the risk of regurgitation and refusals.

Seriously, just feed your snake where it's comfortable and lives. Not even my hyper-aggressive will eat anything king snake thinks that just because the tank opens and I reach in he's going to be fed. Because I take him out and reach in for reasons other than feeding and reptiles aren't bright but they're not THAT dumb.