You should try the ZZ alone on the rope, nothing added to it.
My first experiment was with an access rope, 10 mm, hard lay. Not good, it grabs but gives a very jerky release. So I put it aside and even gave some bad mouthing about it at some moment.
Not very long ago, I wanted to try again, but this time with my new climbing rope/ long lanyard, Xperience by Edelrid, a 16 strands, almost 1/2". The ZZ was intended to be dedicated to it, ddrt mode, but that got some delay because the rope waited a splice since a looong time. It was ready when I polished some improvements in my technique, blocking down a spar, tying on a down sloping limb and fighting the rope's tail stuck under the limbs for examples. Having the possibility to convert the ddrt to srt on the fly was a sweet answer for this three points, nicely allowed by both the HH and the Akimbo. But that was only for the main rope. I found that if the secondary rope could do the same, that should multiply the possibilities. Let's try the ZZ in srt, as is, to avoid messing with some other gear in the tree. So... to my great surprise, it worked fine, smooth release, good control, even with just one hand. To go up, my neck lace holds the ZZ by the ddrt hole, with the same setting than the Akimbo, so I can switch as I want. So cool.
I'm a slow moving guy, so I can't guess what the "nearly free fall guys" would find about it (heat release ?), but so far I'm very pleased.