At the suggestion of a Facebook commenter, I've decided to start backing the target up incrementally on the Glock 37. Since I'd fired 370 rounds and had a fifty-round box of Federal HST on hand, I ran the target out to ten yards and loaded up thirty rounds. This would leave me ten rounds for a chrono string and enough left over for a couple five-shot benched groups at 25 yards.
The Glock 37 has now fired 400 rounds since it was last cleaned or lubed, with one parts breakage. 1,600 rounds to go.