Skylab as lunar gateway?

Hypothetical question: Suppose the US had continued its agressive plans for space exploration after Apollo 11 and had decided to establish a permanent presence on the Moon.

Would it have been conceivable to have Skylab II (the Skylab backup which ended up in the Smithsonian) sent to the Moon as an orbital lunar waystation, much in the way of the cancelled Lunar Gateway?

IIUC a two-stage Saturn V derivative called Saturn INT-21 was considered to launch Skylab, with a LEO payload of some 120 tons. Without the CSM (which could be sent later on on its own), and shaving off the Apollo Telescope Mount, Skylab would have weighed around 65 tons. Would that have rendered enough delta-V to fly Skylab to the Moon?

I guess the lack of restartability and storable propellant of the S-II stage would have been an issue for braking into lunar orbit? Any other significant problems?