I have a similar problem. My strict chin ups, and neutral grip pull-up are 6 solid reps on an all out set, but only one strict pull-up. My mixed grip is about 3-4 reps each.
I am heavy, at about 250lb. My max hollow hang is 3.5 minutes so grip is not an issue. I do higher rep half and full kneeling Lat Pull Downs to try and bridge the gap with different attachments, and use band assistance on pull-ups.
Hey George...
Pull-ups have always been a staple for me. A couple of things I have learned (at least from my perspective) are:
Pull-ups require one to engage the whole body whereas Lat Pull Downs do not.
Bands are an option but in my opinion not so effective as one gets diminishing returns the higher up you go. Some folks have their sticking point near the top, where a band is typically of less use.
One thing that I think is top notch for pull-ups is using a pulley counterweight system. I mention this to you because I know that you like to 'tinker' with building cool and unique training tools.
With a counterweight system one can add or subtract whatever weight needed to make the desired reps. It allows for a fine degree of weight control, and the force is constant throughout the full range of motion.
This method works wonders, for pull-up enthusiasts of all levels. It's ideal for people recovering from an injury, people trying to get their first pull-up, and those trying to bridge the gap between reps. I also think that it is a superior method to train for the elusive One Arm Pull-up (elusive to me at least)
The drawback of course is that one needs to build stuff with pulleys, ropes, and such, as well as have a suitable structure to attach everything to.