Which pedals?

[TsPoet]

Only issue I've had is that sometimes I feel like my cleat is loose, but when I go and check it, it's not -- gotta figure out what's going on there because it's distracting.

Some describe the feeling of riding on eggbeaters as similar to riding on ice. I get that, too. It's the float. You can get used to it, it's a good thing, really it is
Also make sure your cleats are whichever way makes for less float, that might help the feeling of riding on ice.
I notice the feeling when I've been riding my trike a lot. My trike has powergrips which, oddly, have less float. So, when I go back to my road bike with the eggbeaters, that cleat is loose feeling takes awhile to go away.

[KnottedYet]

I clipped out with my right foot first for 25 years with toe-clips.

It seemed perfectly natural to clip out with my right foot with my cleated pedal system. (aka clipless)

I can clip out with my left foot first when the need arises.

When I ride on my platform pedals, the right foot nearly always hits the ground first.

Do whatever works for you.