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Turning down the ai_line_modifier by 0.01 or so might help, but that's not a good solution long-term. Recreating the LP files is probably a better solution. That's far less scary than you think (especially since it's not the race.lp), as long as you have a wheel and are a reasonably smooth-ish driver. I say smooth-ish because if my crash prone self can do it, pretty much anyone else with a wheel can, too.
If you want to experiment... (back up the minpit0.lp file first), make a copy of pit0.lp and make it minpit0.lp.
Assuming you don't want to mess with .LPs, which I get. But if you can redo the minpit0.lp, absolutely do it.
I think with something like that I'd start with opening the track.ini turning ai_line_modifier down by .05. Either that or making a copy of pit0.lp (assuming there aren't two pit lanes) and renaming the copy minpit0.lp. The existing minpit0.lp should be backed up.
If that doesn't work, consider moving the AI merge_to_pit_line back a tiny bit, but that can create a whole different set of problems. So avoid that for now.
If anything I described sounded obtuse, don't hesitate to ask for clarification.