Lately i've been doing chins as the first exercise on back day. It seems though i have not really progressed though. I can do body weight (180-185 lbs) 8, 6,4 reps over 3 sets. I use a grip where the palms face each other. It feels like my biceps are failing out without really getting at my lats. I thought about dropping reps and trying to fail out at 4-6 on the 1st set. Right now though my lats can keep going so i've been adding a set or two of pulldowns.

My goal is to be able to do weighted chins (i have a belt) and have this be one of my main progressing exercises. I would like to tear my lats to shreds each back day achieving maximal stimulation and growth.

One thing i though of is i haven't been doing any direct bicep/tricep work for a while. Would this be a good reason to start? how should i fit it in?

Right now i do (2-3 sets each exercise)
day 1-squat, leg press, leg ext/curl
day 2- rest
day 3- db bench, incline, weighted dips
day 4 - rest
day 5 - chins (+pulldowns), rows, shrugs
day 6 - rest
day 7 - db OH press, front raise, lat raise
day 8 rest

many thanks!