We had this problem a bit at the start where he couldn’t get the cage on as he got hard before but it’s not really been a huge problem, we just wait until he’s down and go quick! We’ve never had to ice him down or anything. Him going to pee just before seems to help turn off the sexual response for a few minutes, or a shower.
But there are two specific tricks, one is lots of lube, silicone lube is your best bet, in the cage and on you. You need it for comfort anyway, and don’t need too much. The other is the ‘Stocking Method’ as described here: