As an amateur mechanic (mostly cars), I've found wearing medical gloves (esp. the more expensive nitrile ones) helps a lot with keeping my hands clean. They tear open on sharp stuff of course, so you'll probably have to replace them several times, but it's better than not wearing anything, and gives you more tactile sensation than the thicker "mechanic's gloves".

I've found nitrile to be pretty durable - they're meant for protecting against needles and scalpels and things, so I'm surprised they're tearing on you?

They are durable, very durable, compared to vinyl and latex. But they're not some kind of exotic metamaterial; eventually something will tear them open, and car internals can be rough environments. The much-thicker mechanics' gloves are more durable for a lot of that stuff, but they really limit you because of their thickness.