To avoid having to re-do the cleats in a day or two, I'd clean the screws and holes with isopropanol and use blue (medium) threadlocker.

If you wish to avoid threadlocker, you could use Crisco, Vaseline, gear oil or even a drop of motor oil for now, and then in a few days clean and grease with your new stash of Park grease.

Park grease is from what I hear a good product, but there's nothing magic about it.