They can live for up to about 3 weeks off the rabbit. 3 doses of revolution should be more than enough time to get rid of them. I’m pretty sure like most mites, they are species specific, so they wouldn’t be able to live on anyone else, like the humans in the house since you said you don’t have any other animals.
If it’s possible with your set up, if you can keep him out of carpeted area’s it will probably be easier to get rid of them. Since any that don’t get vacuumed will be dead at the longest 3 weeks. As far as his cage, I’m not sure what kind of bedding you are using right now. But if you are using rugs, or things that are hard to wash, you might switch to some fleece throws for the time being. Those are easy to run through the laundry regularly. You can probably just get it really cheap from a second hand store and toss them after use too.
Any wood, wicker, cardboard, paper I would toss. Keep things a little on the sparse side for a few or keep toys things that you can easily toss after a few days use. Keep all your things that can collect mites/eggs out of reach during treatment as well.
Cages always have little nooks and crannies, so wipe down well, or if you can take it outside and pressure hose it clean or drag it into the shower and do so.
Hay, pellets, litter I would keep out enough for a couple days at most so you don’t have to waste much by cleaning more often than you would otherwise.
Keeping things simple always seems the easiest for me, with things like this.
as far as having to use ivermecin..I haven’t had to use revolution on my bunny, but I’ve used it on my rats and in the past ferrets and in my experience it works far better than ivermectin. Knock on wood, my hope would be it’s the same for bunnies.
If you are really really paranoid…You could move him to a completely different cage in an area of the house he doesn’t normally have access to during the treatment period. Then when you move him back you can be assured his normal cage is completely free of mites. Maybe a bathroom and a travel cage?