Also consider doing two arm pullups, but shortening the length of pull on one side. This is achieved by doing a wide grip on one side, but standard on the other. When you shorten/contract one side partially, you hinder the amount of work it can perform, biasing the side that is performing full range-of-motion.
This is also one of my goals, and I am working towards it by executing pullups using a bar that has a gusset of 45 degrees coming off the pull up bar. This allows me to bias one side.
You may not have access to a pull up bar like this, but get creative by using a band or the like.
Law of diminishing returns applies!
Plateaus are always hard to deal with. Given your workload, it appears as if you are concentrating on strength when considering the strength developmental continuum. Because of that law, your body has become efficient working at the repetition range. Staying here will eventually mean a decrease in performance.
Your choice is then to move to peak power and strength, increasing the weight and decreasing the repetitions in order to become stronger, or decreasing the weight and increasing the repetitions to increase endurance.
I would move to decreasing the repetitions to focus on strength for about two weeks (more weight, less reps, closer to 4 reps than 6). Upon that point, and depending on your results from that microcycle I would continue along either an undulating periodization program (strength one day, hypertrophy another, endurance another) or a traditional (endurance, hypertrophy, strength, power, peak strength, peak power, in that order).
The law always applies, so you've gotta switch it up.