Brad, adding bleach to every fill is a bad idea
Any purifying properties in chlorine evaporate within 24 hours, leaving only the caustic properties in bleach behind. So adding bleach to every fill is damaging to the system, but does nothing to keep the water from becoming foul after it sits. A teaspoon per 10 gallons is heavy dose, btw...enough to make your water taste and smell like an over-chlorinated swimming pool, which defeats the purpose filtering the taste of chlorine out when you fill. Filtering removes foul taste and smell, but doesn't remove the source(s) of it--the molds and fungi that accumulate in the plumbing. So my advice: recommission the system every spring according to the directions in the "Fresh Water Maintenance" article in the Head Mistress forum reference library to get rid of those li'l critters...that'll keep your water smelling and tasting as good as what comes out of the faucet on land. If you feel you need to improve on that, then by all means, install a filter on the galley faucet. However, a filter cannot be a substitute for maintaining the system, it's only an extra added improvement.