The involvement of those smaller shoulder muscles is why deadhang chins are better for overall shoulder health.
Also, the lats actually are always under constant tension when performing chins (partial ROM or deadhang) as they originate on the spine and scapulae and attach to the Humerus and at no point do they detach from either of those two points). What changes is the degree of leverage that they possess and the number of Actin/Myosin cross bridges that are in contact at different points along the ROM. What you are essentially doing is staying within the "strong" portion of the ROM (where your lats have good leverage and a good number of cross bridges in contact) to allow yourself to get more reps (and yes, keep the muscles under tension longer). This would be akin to performing quarter squats or top 1/2 bench presses to get more reps and keep the muscles under tension longer.
Which is fine to do if that fits your goals.
Again, you are getting more reps because you are never forcing the lats to work outside of their "strong" ROM, not because they are under constant tension (which actually should result in fewer reps in theory as implying non constant tension would be definition mean that the muscles are getting to rest between reps).
If you are really worried about the forearms/grip limiting the amount of effective lat work during deadhangs, then just use straps (that's what they are designed for). Or, realize that your shoulder mobility or grip strength is poor, and that you need to work on it (if strength or performance was your goal).