Amazon sells 1" HTH[pool chlorine] tablets that fit in the strainer. I used to put 3-4 everytime I changed/cleaned strainer to help kill/eliminate any bacteria in A/C seawater lines. I do not use it on Catalina because it is run only on dehumidify, so it stays clean.
Another useful trick is to buy a spare strainer so you always have a strainer clean & ready to go as it reduces the amount of time you must have AC turned off which your crew will appreciate.
Will also give you more time to properly clean strainer you just took out!! If strainer was fairly clogged, you can leave it overnight in a soapy bucket which will help reduce effort needed to clean it!
The installation of the seawater line off of the AC seacock sounds interesting. I would make sure you have a seacock on the second line so you can shut off when not in use for two reasons:
Reduce any issues with second hose leaking, when not in use;
Use as a method to backflush AC system with fresh water and some cleaner - control inflow from freshwater at seacock entry instead of at washdown spigot. While you would normally close thru-hull seacock for the reverse flush, I would finish reverse flush by opening the thru-hull seacock as thru-hull may also need cleaning/flushing. Could also be used, at a marina, to undo any plastic bag that may have been sucked into thruhull and is not released when you turn pump off - saves you a dive to remove plastic bag!.
Another trick to help store fenders in starboard aft locker, is to put a loop[I used a plastic pipe holder] so you can put one of the fender lines through the loop and do not have to dig in to pull out fender[s].
Summer is coming up so I wish everyone in North a speedy spring cleaning as I know you have a short season. We had a power boat in the Great Lakes for 4-5 years as well as a Catalina 22 in Moosehead Lake Maine, so we know how nice but short your season is!
May you have Fair Winds & Following Seas in 2022!