On any foul where we'll stay in "this" end to shoot free throws, we always switch. If I'm the lead, I'll get them lining up and collect the ball, then move out to trail. I'll bounce the ball to my partner when he gets back. If I'm the trail, I'll move down to lead, get them lined up and collect the ball. I always move around the players, rather than through them, so that I can watch them all (as much as you can watch 10 players who are all moving). If there is any hint of trouble, or the foul was a hard one, then I'll generally freeze physically and watch until I feel comfortable that there will not be any non-basketball stuff. Generally this flows very well and the switch does not delay the game.
The long switch is kind of an odd animal. I've tried pre-gaming not to do this. The long switch I'm talking about is where we're in a half-court, there's a foul and we're going "that" way. I believe it's better to not switch on this foul, because that puts both officials in "this" end and all the players going "that" way, with much less supervision than they should have. But it's just too much of a habit to do the switch, and I finally gave up trying not to do it. It'll probably bite me at some point
In the situation where we're already at opposite ends, like a foul during a press press or after a time out where the throw-in is in back court, if the foul is in back court, we're staying put.
That's what we do around here.