Taking into the account that I only used the edge of the board, I decided to use the center of the board to see what I could do. And, yes, ignoring promotion rules, I actually WAS ABLE TO get 7 white pawns on the same file. The game ends just before the white pawn is set to capture the black queen, completing a 7-solider line. I even managed to cut off several moves.
I guess just consider this a self-question-and-answer for the entertainment of everyone else.
UPDATE 3/3/19-I have found an extremely quicker version than the one below. It also ends just before the white pawn is set to capture to get on the 8th rank. I will leave my old, 83 half-moves game for comparison. Welcome the new 37 half-moves game!
UPDATE 2 3/3/19-Thanks to the help of @DM once more, the perfect 7-same-file pawn chain game has been created. It is know the same number of moves, but there is not a single wasted move. No, the white h-pawn movement is not a waste-it is a nessacary filler move. Now, here is that perfect game!
UPDATE 3 3/3/19-Using black pawns, once again thanks to @DM for this idea, we have completed our quest to find to find the perfect 7-same-file pawn chain. We used black as to shave off half a move. Now I present to you the perfect game of our goal, in just 18 moves, all necessary and no moves wasted at all!
1. d4 b6 2. d5 a5 3. d6 exd6 4. Qd5 c6 5. e4 cxd5 6. b4 f5 7. Bd3 fxe4 8. c4 exd3 9. c5 bxc5 10. Be3 axb4 11. Nc3 bxc3 12. Bd4 cxd4 13. O-O-O g5 14. f4 gxf4 15. Rd2 cxd2+ 16. Kb1 f3 17. Ne2 fxe2 18. Rd1 exd1
My old 83 half-moves game.
1. Nf3 d5 2. Ng1 d4 3. Nf3 d3 4. exd3 e5 5. Ng1 e4 6. Nh3 e3 7. fxe3 Qd4 8. exd4 c5 9. Ng1 c4 10. dxc4 Be6 11. Nh3 Bd5 12. cxd5 Nc6 13. Ng1 Nb4 14. Nf3 Nd3+ 15. cxd3 O-O-O 16. b4 Kb8 17. a4 f5 18. g3 f4 19. gxf4 Bd6 20. Ng1 Be5 21. fxe5 Rd6 22. exd6 b5 23. axb5 Ne7 24. Nf3 Nc6 25. bxc6 Rd8 26. Ng1 Rd7 27. cxd7 a5 28. b5 a4 29. b6 a3 30. Nc3 a2 31. Rb1 a1=Q 32. Nf3 Qa7 33. Rb2 Qc7 34. bxc7+ Ka8 35. Ne5 g5 36. Nf3 g4 37. Ne5 g3 38. Nf3 g2 39. Ne5 g1=Q 40. Nf3 Qg8 41. Ng1 Qd8 42. cxd8