Clean, cold barrels on average will typically shoot higher than a hot, fouled barrel. Your M1917 is not unique in this regard. A lot of people I know at the range only test their handloads in clean/cold barrels - i.e., they clean after every shot and let the barrel cool. I've never gone to that extreme.

All my rifles will do as you described. The first shot is usually an inch or two high at 100 yds. They group well after that. I always throw the first shot out of the group when load testing. I also use the Optimal Charge Weight (OCW) method of shooting one of each test load at a target and rotating through all the various loads. That way, each test group is equally affected by barrel heating and fouling.