You have done a pretty good job of troubleshooting the problem. Since water is getting past the thru hull, and the water strainer is clear, the the problem is most likely the water pump.
You fixed the loose belt, so that leaves the impeller as the likely problem.
On my boat, I can get to the pump fine, but the pump cover is on the back side, so I have to remove the pump to change the impeller. I disconnect the hoses and remove the pump on its bracket.
It's easier to change the impeller working on a table. Be sure to lube the new impeller (olive oil works well) before you put it in. Make sure you retrieve any broken impeller blades that might be loose in the case or output hose.