With this method, you complete as many technically correct reps as you can in the 4-6 rep range. Your goal will then be to double that number of reps. To do that you take short rest periods (rest-pauses).
For example, let's say that you get 5 reps in the initial bout. This means you want to do 10 total reps for your set. After your 5 reps, you'll rest for 15 seconds. Then you might get an extra 3 reps. This means you'll need to get 2 more reps. Rest another 15 seconds and then you'll be capable of getting the last 2 reps.
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Check out this single-leg movement that provides all the benefits of unilateral work while still allowing you to go heavy.
If this list can't convince you to include at least a bit of fast lifting in your routine, you might want to seek professional help to discuss why you're avoiding maximum success.
Fix your posture and correct all those imbalances caused by too much benching. Nails your core too. Take a look.
If you avoid weighted pull-ups, you're also avoiding bigger lats, better arms, a stronger core, and a truly functional body.