Go with exercises that are effective for the areas you want, as you've done. Forget the by-the-book stuff some adhere to that tell you that certain exercises are essential, even when ineffective.
Before giving up on an ineffective exercise, first try using different form. Enlisting more biceps is typical of using the wrong form on pullups: the better way involves pulling with the elbows, with less upper arm flexion, and will enlist the lats more.
Then try variations involving different grips, different grip widths including close-grip triangle bar and medium grip, as well as different angles-behind the head instead of in front, etc. If you can find a good version you can keep doing the exercise, either alternated with the other one or supersets using both.