I'll give that a shot. I'd still prefer another method if anyone has one since it'll make it harder for me to make the minigame GUI setting a scalar multiplier on the respawn time down the road.
EDIT: doesn't work; the centerprint is determined at the moment of death but whether or not clicking will respawn the player depends entirely on the time elapsed and the current .respawnTime of the mini at the moment of the click. I suspect it's based on a sim-time subtraction, and not a schedule, which explains why nothing trace()s out server-side when respawn becomes available for a player.