Pascal,
There's only about 3 1/2 inches between my strainer outlet and the pump's inlet, and the hose connecting the two runs slightly uphill. Still, I was unable to successfully re-prime. I cracked the bleed valve on the discharge side of the pump, and it had a steady stream of water coming through it, which led me to believe there was no air in the system between the through-hull, and the discharge side of the pump. From there, all lines run slightly uphill to the A/C unit, with no kinks, loops, elbows, ect.... In other words, the system is properly installed on this vessel. That said, one of the "downstream" lines must be air locked. I moved them around while running the A/C unit in an effort to migrate any air out of the system, to no avail.
In the interim, due to plumbing constraints on the supply side of the pump, I'm going to try what Harlan suggested above, and connect a hose to the discharge side of the system to back flush water through the entire loop to get the air out. It appears that the A/C discharge hose dumps right into my shower sump, which is easily accessible on this vessel. That said, if this method works easily, I'm going to connect a permanent hose fitting to the end of that hose, so as to easily have a connection there for future use.
Prior to doing this, I am assuming there is no problem for the pump to receive a backwards flow of water. (I'm thinking about the pump's impeller vanes in particular.) I'll check with the vendor, or seek advice here from others who may have utilized such a method.
Thanks to all for the guidance so far. Any comments or further suggestions/advice?