But he keeps coming by and begging to work things out.
You dumped him. He thinks that is negotiable. To me, that's a red flag. Part of the sickness. Healthy people respect boundaries. He's stomped all over yours by lying, cheating, conspiring to cheat, using METH behind your back, and now not taking no for an answer.
He has proven nothing yet. Like the others, I suggest letting him prove to you in the long term that he has the chops to live a sober and productive, happy life, and THEN you take the temperature and see if he still looks like a viable catch.
A year is a starting point. Your life has a lot of years in it. How many of them are you willing to sacrifice to life with an active addict?
If I may make a suggestion -- why is cheating a dealbreaker, but meth addiction isn't? There's more here in you that's worth probing.