Would too-small grips be why my arm and hand are cramped and tingly at the end of even a half-hour ride? I don't think I am gripping too hard... The other possibility is that my gloves may be too tight/restrictive.
It's possible. If you're new to riding, it may just take a while for your body to adapt to long periods of a rather unique position. Other than that, I'd say if you're not comfortable when you get on the bike, it's going to be worse after riding for a while. If your gloves have been broken in and they feel too tight, they probably are, but remember that new leather will stretch a bit and conform to your hands as they break in. There's nothing better than a properly fit and broken-in set of gloves. That's why people never want to get new gloves.
As far as grips are concerned, you can always go the motorcycle store and just grab onto a bunch of grips and see which feel best to you. I prefer a larger diameter, and a fair amount of cushion, but I know some people prefer smaller diameter, harder grips.
Also, when you're riding, just visualize and think about where you're uncomfortable. Take one hand off the bar and hold it a little higher, or a little bit further back, see if maybe a different shape of handlebar might feel better for you. Uncurl your hands as if using a larger-diameter grip and see if that feels better. Swap bikes with somebody and see if it's more comfortable for you, and try to figure out why that is. You can get rear-sets for the footpegs, all different kind of handlebar shapes, grips, the Corbin seat is available for Zeros now, there's a lot of customization available. The trick is to figure out where your problem areas are without spending a ton of money trying all the different possibilities.