There is no loophole.
It doesn’t matter if you ask for flight following, ILS, RV, VFR, Visual all in succession, they’re all the same endgame and they’re all duplicates even if the wording is a little different.
When you took off, patternwork was not available for a reason. The approach controller knows Tower isn’t accepting patterns. The departure controller knows Tower isn’t accepting patterns. Bouncing around the frequencies does not change a thing.
The denial of entry message means go somewhere else. it does not mean “hover around interfering with every other inbound making the same request that was already denied four times every 30 seconds.”
No patternwork is not fungible. It means your destination will not be your location of departure, so get over it and go somewhere else.