I used to go to a lot of trouble to overlap and lock the stings.. but then i just got lazy I suppose, since then I really haven't noticed any difference 🤷... I remember watching an old video of Rory Gallagher and how he strings up with a once over then under. It looked clean and is probably best practice.. When I'm in a rush I don't bother, but if I'm doing a big clean of one of my guitars I'll occasionally string it up like that.

Hi Luc P, ya I've had similar intonation issues with my Taylor GSmini. I've had some luck by bringing it in to a good luthier. He adjusted the truss rod and change the frets which seemed to sort things out for a while. But i'm traveling a lot with that guitar and all the humidity changes haven't helped the situation.. So it's now gone back to the way it was.. But either way, I think you're best bet is to get it checked out by a decent luthier. Hopefully that does the trick. Another option would be to try different string gauges. If you're using heavy try medium and if your using medium try light. That may help a bit. It really depends on the guitar.