I ride in rainy conditions quite a bit and don't have waterproof gloves. I usually ride with a pair of long-fingered gloves made of neoprene and have a pair of warmer cross-country skiing gloves in my back pocket. If/when one pair gets thoroughly wet, I switch to the other.

I would argue against the surgical gloves because of the sweat issue that others have pointed out. Getting wet from the inside is no better than getting wet from the outside...

Cross-country gloves can be much cheaper than cycling gloves for the same type of quality/function. I know they're not easy to find in California, but looking online should make it easier...

This is in September, right??

Good luck!