I was just noticing that the leviton cube taps that I bought at my local lighting/grip supply house are only rated 15A rather than 20A.

Anyone have a source for good small 20A cube taps?

Why, are you wanting to burn down a house?

I don't think you are going to find 20 AMP rated cubetaps.

If you are running incandescent lights with this stuff (high draw)
and need to split, you'd be better off going with stage-pin connectors.
Then use what is know as a 'two-fer" or "2-fer".
Adapting back to high quality Edison plugs that are rated for 20 AMPs if plugging into wall power,
but you better be careful. Fires are not good, especially if the building isn't yours ;-)

Or build yourself a reputable quad box: two 20-amp duplex outlets in a metal "handy-box" with a short pigtail terminated in a 20-amp male plug. And make sure all those connectors (and wire) are really rated for 20-amps, don't substitute 15-amp connectors to save a few cents.