Save yourself future aggravation and go ahead and get a new water pump. You can try to band-aid it, but you are just looking for more failure in the future. I replaced my pump that intermittently cycled when no water was running about 3 weeks ago. I messed around with the old one for almost 3 years trying to figure it out. Sometimes, you just need to go ahead and bite the bullet and "do it!" and get it over with.
I replaced the exact pump in my camper. Total cost was about $125 from my local dealership parts store. They had other models, that ran less than $50, but I wanted to keep the same identical pump. I'm one of those "crazies" that believe in keeping everything fixed with factory replacements. But you may be a bit more sensible, and opt for the less expensive one.
Either way, save the headaches and switch out the pump. It really is not difficult at all. It took me about 30 minutes to do it. The biggest problem I had was moving lines around a little, because I wanted to reposition the pump for a little easier winterizing access. I also added a longer winterizing hose and new clamps (part of that $125).