Having trained myself to a 1APU, I can tell you from experience that you’re up against it. 3 months probably isn’t enough time given your weighted PU numbers.
That said, I think the daily practice Xen suggests offers your best chance. If you had more time, I would recommend rotating though several progressive templates, with important deloading periods to spare the joints. But because you only have 3 months, your best bet is to build strength by practicing the movement itself.
Negatives are great, but in my opinion represent only one aspect of a successful 1APU program. The 1APU in particular requires strength from the bottom up, and negatives tend to be “top-loaded” – slow up top, then dropping like a rock. If you only do negatives, you’ll probably neglect strength at the bottom of the movement. Add isometric pauses in 3 positions (the 3 sticking points): the bottom, with your elbow flexed only a few degrees; the middle, elbow at 90 degrees; and the top, with your chin just over the bar. Try to hold each position for 2-4 seconds, several times per day to ensure strength through the entire range of motion.
If you train 3 times per day, I would suggest doing maybe 4 regular chins slowly to warm up. Then rest a couple minutes before doing a negative. To make the negatives more effective, I recommend performing them in a variety of ways, the major 4 being: standard (slow and controlled through the entire movement), top emphasis, middle emphasis, and bottom emphasis. With the latter 3, move yourself as slowly as possible through the emphasized range of motion and merely control your descent through the rest of the movement. Do one of these in each training session, being sure to attack your weakness. Then move on to isos. Then just hang from the bar for a few sets to strengthen your grip and stretch your lats (and chest and bis).
Take a day or two off whenever you feel like you need it. Expect joint pain, but don’t let it get so bad it keeps you from training and getting stronger – obviously, you can’t win a bet if you’re injured.
The true 1APU, in my opinion, is at least as complicated as a squat, so there is much more to say, but time is precious for both of us. You need to get training, and I need to get back to work.
If you’re still at it in a month, check back in.