Odds are, with 4 deeps, there will be another Qcell or three. Remember that hive is trying to supercede that queen. She really needs to go into a nuc/single deep of her own. "Swarm" under your control.
Finding her is gonna be, ummm, interesting.
Because the Qcell is still unhatched, they may not have started to chase her (slimming her so she can fly).
Have anybody close that can help you queen hunt? Empty box to move checked frames to helps. Go top to bottom, look for fresh fresh laid eggs, odds are she is close by. After today, she could be running anywhere to inspect what changed.
Did have similar issue this spring with double brood box. Queen had already been slimmed, didn't see her when put qcell frames in nuc. Did another just for good measure. 2 days later original double swarmed while I was 2 states away. Talked mama thru her first swarm over phone. Next day neighbors Russians decided to drop off a present in her peach trees. At least she had idea what to do next. Gathered both that night when back from Miami. Next day did another "force split", up from 1 hive to 6 in 72hrs. If they want to supercede, they will. Can u "guide" them, yes. Outsmart 60-80,000 women. Just tell them that new hive body is on sale, and,the latest greatest thing since sliced bread, and in a better neighborhood.
Throw in the pool if they ask about it too.
Queen hunts are a grind. Dont feel bad if you end up nearly cross-eyed. Goes with the territory.
My secret weapon is a fellow beeks wife. She has the creepy uncanny ability... "There she is!!" Every time.
Good luck. Let us know how it goes