Are you sure you're not getting this confused with the parking garage being built for Cabana Bay? There's nothing anywhere about a second parking garage being built on Universal property, but there's plenty of information out there about the Cabana Bay garage.
For example, it received FAA approval a few days ago:
https://oeaaa.faa.gov/oeaaa/external/searchAction.jsp?action=displayOECase&oeCaseID=189905587
And it has the same 6 month construction timeline you quoted. And it will also be 3 levels.
(ground level plus 2 elevated levels.)
I'm not doubting your sources by any means, I just find it odd that for a project that's apparently so close to breaking ground there hasn't been an appearance of a permit, NoC or FAA approval. With the Cabana Bay garage just getting its approval on the 20th of June, work scheduled to begin very shortly, and those similarities, could it be possible that that's the garage and your source was mistaken?