The K6 is not programmable out-of-the-box, but it seems some people have successfully installed QMK firmware on it (with caveats); https://github.com/CanUnesi/QMK-on-K6/

If you just want to try the numpad thing out, it might be easier to use something like AutoHotKey. Here’s an example of a script that uses CapsLock to toggle the numpad layer.

Of course, AHK scripts only work with the computer you’ve installed them to, whereas using programmable firmware will work regardless of which device you connect your keyboard to.

I do have to grind through entering a list of numbers

Have you considered a numpad layer? They’re great. All of the speed and convenience with none of the wasted space or extra arm movements.

I have a numpad for both hands on my Redox :-)

*whooosh*

IMO Steam Deck is the best overall option, as it’s beefy enough to run PS3 or even Switch games.

If it’s too heavy, the Retroid Pocket 3+ is a decent emulation competitor with a lighter, smaller form factor.

I find myself constantly switching between them all and can’t settle down to actually play a game.

This sounds like one of those problems where buying more hardware doesn’t help. Ruminating about the “best” handheld choice is an easy way to forget about playing the games themselves. I’ve been there. The solution is to just pick a device at random, and go outside to play it. There will be pros and cons, but if you’re not even getting to the point where you can actually play the game, then the pros and cons don’t matter either.