I think the most challenging part of your questions is "Complete". I started with a list of PSA "company sets" and looked for sets with 1-3 set builders, then took a look for a few I know are tough. Here's what I came up with:
1953-54 Briggs Meats - Top set 82.5% complete. 33/40. 220 total graded (192 "A") - not as rare as I thought. most players with single didgit pops
1954 Blossom Dairy Charleston Senators - 1 set 100% complete. 22 cards. 1 of each graded. Has to be a winner or tied.
https://www.psacard.com/pop/minor-le...enators/126126
1954 Stahl Meyer Franks. Top set 100% complete. 12 cards. 164 examples graded (100 "A" or "1")
1958 Kahn's Weiners - top set 100% complete. 29 cards. 140 total graded.
1962 Bazooka complete boxes - top set 60% complete. 15 cards/boxes. 32 examples graded. 6 pop 1's, 6 pop 2's - another super toughie, but not completed by anyone.