Hey OP, I have a friend who scheduled a micro wedding and they googled terms like "city hall san francisco wedding photography" or looked up vendors featured on instagram with city hall. Those people are more likely to be flexible and agreeable with doing smaller time frames/simple packages. You may also have more luck on unconventional days (Fri, Sun, etc) or during off season because Saturdays during say, summer might go to bigger bookings. My friend in SF has beautiful photos for like $1500 (but winter 2021, so prices werent as steep).

Fwiw I'm planning a wedding out of state. Photographers there full day are generally around $7,000. Some sites have special sections for elopements and those prices are more around $2200-2500. It's generally one of the highest expenses for a wedding, but a lot goes into editing and such. You may find it worth it to splurge if you want a certain look for your photos, but if you aren't particular you may be able to get something very cheap. I think you will probably pay a minimum of $1000 if that helps (but I haven't looked at the market here specifically).

edit: look up terms like "elopement packages" "microwedding" when searching for a photographer and it should help you narrow down a bit