I have used both with no real preference. I caulk the hole so I can poke it out and use that hole as a blow hole to seat the bead, then re-caulk. You mean pushing in on it and out a couple times won't do that? If not, I'd imagine unseating the bead just at the beadlock on one side would do it. Keep in mind you'll need ramps wedged in to the opposing side to get that tire off the rim bead there, or you're going to break the bead of the tire.