I realize this will be called totally heretical and will have people like Poliquin having fits, but chins and pullups are NOT always the best exercises for increasing chins and pullups.
For trainers other than novices, periodization schemes which include training as light as 60% 1RM, and building up gradually to at least 80% and perhaps 90% of 1RM, is much more effective than training with fairly constant heavy weights.
By training for chins and pullups by doing those exercises, where in your case this is a pretty high percentage of your 1RM, you aren’t getting the benefits of periodization.
Now, how to do a comparably good and similar
exercise at lower percentages of 1RM?
The problem is most machines suck. However,
in my opinion the Med-X Torso Arm machine
has correct motion and strength curve for
training for wide grip pullup and works
extremely well for this, and the Avenger
Pulldown similarly is excellent for training
close grip chins. With these machines you can train progressively which is very helpful (this may be an understatement) to success.
You can indeed do chins and pullups if you prefer once you get to the heavier part of your training cycle, but these are preferable for the lighter parts of your training cycle.
If you want to reject this advice as being
unmanly or something, then there are two
other approaches that can help with the
traditional exercises.
On the last set of your exercise, lower yourself very slowly, as slowly as possible.
On the next workout, perform all previous sets in like manner (don’t go for extra reps or do at different speed, use same rest intervals etc.) but try to do the final negative even slower. When you get to where the final negative lasts 30 seconds, then you are ready to do another positive rep in your set.
I’d also by the way suggest that given
the pattern of reps you’re achieving and
the number of sets you’re wishing to do,
you should aim for only 3 reps for the first
few sets, for now, and do only as many
sets as allow you to achieve 3 reps.
Take 4 minutes rest between sets.
Another approach is to, no more than once
a week, do a couple of sets of negative
chins (using a bench so your legs can
push you up to the top position) doing
about 8 second negatives for as many reps
as possible, ending the first set when
you can no longer do a 4 second negative,
and ending the second set when you can
no longer keep the negative above 2 seconds.
Another important point is to really focus
on the quality of the top position. Your back
should be arched, for chins the bar should be as low on the chest as possible, the shoulderblades should be squeezed together, your chest should be thrust out as if you were a Playboy bunny pushing out her rack for admiration, you should hold this top position for at least a second, and your upper body should be leaning back as much as possible at the top. (Don’t use leg work to swing your way up, either.)
Stick with it and I’m sure you’ll succeed!