The only way I can think to really get him to pivot on his hinder is to workin in small steps.
You can also teach him to yield his front end away from you, in which you don't release your cue (I use a carrot stick to tap the shoulder or neck), until he crosses over; ie yielding the front end to you. Only ask for a step or two away from you at first (in the correct manner), and build from there.
Once he knows how to do this, it should be easier to teach him to pivot, as he will likely start yielding his front end every time you ask him to move away from you. If he doesn't, go back to the 'basic' yielding. He's probably just never been taught to yield his front end, so it's something you'll have to teach him
As far as setting him up, as long as he has a good back up in hand, this will be easily remedied. Rather than coming to a stop, and struggling to get him to set up immediately, back him several steps, and ask for a halt; chances are he may stop relatively square. Then just back him, or bump his halter foward (to get him to step foward) gently, in order to get him to square up the rest of the way; be careful to not 'over cue' him; apply very gentle cues, so that he understands to simply pick up his feet and move them slightly. Release the pressure as soon as he picks up his feet. Just keep your sessions short and sweet, and he will catch on. I would do it prior to a ride, and maybe when you're cooling him out, or after he's cooled out. Probably no more than 5-10 minutes per session; for most horses, showmanship\halter, is going to be the most boring thing on the face of the planet so don't over do it whatever you do!!!
Some people will simply get their horses set up most of the way, and then use their foot to cue a front foot to move, or go to the rear, and pick up a foot and move it; I'm not a fan of this personally, but in 'fun' shows, it's probably not too big of a deal. I'd rather see a horse set up nicely with cueing from his handler without touching.