Common names for short, wide terra cotta pots are "bulb pot" or "azalea pot". you might try searching on that.

Maybe make one. Google "hypertufa containers", there are some ideas. That way you can get what you want.

Here's the current pot. I'd like to stay with current style, just bigger

And here's the cactus.

That hypetufa idea is very interesting but I don't have the time.

Local potters? I've gotten beautiful handmade pots, including custom made sizes from local ceramicists, for no more money than retail price pots from big box stores.