Cleaning caliper pistons

I've had that problem on what I'll call "keyed" (as opposed to slide-bolted) calipers. Yours are probably a little heavier than mine were on Ford E-Series. I found that if I could get my knee against the side of the caliper opposite the hub and bear against it, it'd stay close enough to work on. You need to get it into actual position before you reach for the key or it won't start into place.
If you can squeeze the caliper toward the centerline of the axle, it'll want to support itself once you get it into its slides.
Perhaps you could rig a bungee cord around caliper and hub.