The CL police will be screaming but if the system already exists and it seems that it does the easy fix is. Cut a bit off of one of the swimming pool tablets, stick it in the strainer basket, let is set for 15 or 20 minutes. Run the system, close the through hull. Take out the sea strainer basket and the remainder of the tablet.
Another way would be make an adaptor with a garden hose end on it from Lowe's or HD that replaces the cap on the sea strainer. When you are done using the system, close the TH, replace the top of the strainer with the plastic piece from HD, attach a garden hose, flush the system with fresh water, replace the top of the sea strainer. This could wait until you are back at the dock.
M/V Stella Di Mare
New Bern NC