What materials would be appropriate for pool parts (chlorine & UV exposure) using SLA or FDM?
Have you thought about using ASA filament? ASA filament is very strong. ASA filament is similar to ABS filament (if you have ever worked with that). When contrasting it to ABS filament, ASA has a higher resistance against UV and chemical exposure. It will also have no problem with the water. Both ASA and ABS filament print at about the same temperatures. 

Here are some links that might be helpful :


UV-Resistant ASA Filament: Properties, How to Use, and Best Brands
Want to Use ABS in Hot Sun? We Compare ABS vs ASA Filaments


Hope this is helpful.