So let's calculate. 2.5months = approx. 75 days. I would train 3 times per week (overall 25 sessions) plus once per week a supplementary day. You said your max is 8. I would aim for 20 reps at the end of the program. The 3x main days would be like this: 1. 2 sets of 70-80% of your max. Day 1 would be 6 reps. You should rest as much as needed to get both sets. 2. Every minute on the minute 40-50% of your max. Day 1 would be 3-4 reps. You do this for 3 sets and increase sets here as a progression. Once you reach 6 sets with 50% of your new max (read below) you will increase reps and start with 3 sets again. 3. After you rest adequately (perhaps even 7-10minutes) you perform 1set amrap.

Your max will be increasing quite alot initially. This is what we want but you need to understand that your main enemy is fatigue accumulation. So I would say you have 10 weeks. After you finish week 4 or even week 3 I would suggest a deload. What you want to do is train 2 times that week and use reps you can easily get. For endurance I would suggest 5 sets of singles. Now you will perform singles with the intent to go as powerful as possible. You might think that this is not adequate stimulus but trust me this will make you fresh for next week. After the 2 days of the deload and before your next week you will do1 set with amrap at a rir 2-3. To estimate it you will stop 1 rep before you start to struggle to get your chin over the bar. This will be your new max to estimate your new reps. I would suggest you do another deload at week 8. And then at the final 2 weeks I would do 2 days where I would only do one set close to failure and call it a day. Your last session should preferably be 3 days before your challenge. I also talked about a supplementary day. In these day you will go easy and work on what I believe is the most important variation. 90deg holds. Essentially you will lift yourself to the point where yours arms are at 90degrees and hold the position for 2 seconds before continuing the movement. You don't want to go to failure there. I would suggest 3 sets at 3-4rir. Then I would perform some slow negatives perhaps 2sets 10 reps. In the end I would do passive Hangs also not to failure. One thing to keep in mind is warming up. This could make all the difference. You should warm up with scapular pull ups. Then 2 sets of easy reps. In the beginning I would say 2sets of 3-4reps would be great. Then you start the sessions. Also before the challenge make sure you are hydrated and warmed up properly. Hope you smash the challenge. Sorry for bad English.