SD - yes, it would have to be a flat, clean surface, with no engravings. I believe that many of the yanmar 2GM, perhaps 2GM20 pumps do have a smooth surface. I just cleaned mine up with a wire wheel prior to re-installing, so it had a smooth bronze finish.
Ultimately, the back plate may be scored as well, but in my case, just dong the cover was enough to improve the water flow volume, and overcome the same problems encountered by the OP.
Proir to doing this repair, I would have to close the seacock while sailing each time, and thne reopen before staring the engine. If I forgot to close it, it owuld start to overheat, and I would have to either:
1. close seacock for about 10 seconds with engine running, and rev engine, to create some suction, or
2. pull off the water line from exhaust elbow and rev engine a coupleof times, to restore water flow.
Since flipping the cover, I have sailed about a dozen times, and have not had this problem again!
Of course, a new pump would be best, but spending $500 on a new pump for an old engine is spending about 10% of the price of a new engine. I would advise tryining the cover trick, as it may increase the pumps efficiency enough to work for many years.
Try pulling the hose off of the (closed) engine seacock, and running the engine from a bucket of water. Measure how long it takes to empty the bucket at idle, and also at a higher RPM, when engine is warm.
Then switch the cover plate, and measure the flow rate from the bucket again. In my case I noticed an improvement, and knew that i had at least improved the pump somewhat.
I also replaced the small phillips head scews (in the water pump cover plate), which are easy to strip, with new stainless allen head screws, from a local fastener shop. A bag of 20 screws was about $6, so now I have spares, if any start to strip.