I've had five VRSC4 and VRCZ4 devices around my home for the last 8 years or so, initially with Vera and more recently with Hubitat. I can't explain any of the above but I share your experiences, and IIRC the same occasional unresponsiveness occurred under Vera as well. That might be notable in that I believe Micasaverde (as they were then) had worked directly with Leviton to integrate these controllers at a more intimate level than any of the open source drivers - for example setting up direct associations from the controller to controlled devices. The combination of the Leviton controller with Leviton z-wave dimmers made for a pretty slick experience, or would have if it worked more consistently!
As for the repeated button press logs, I came to the same conclusion as you, that it was potentially storming the network and interrupting other communications - I would see that other unrelated automations would fail until this apparent storm had passed.
I have to confess that my "solution" in the last few months has been to tear out all these Leviton controllers and replace them with the Zooz ZEN32. My personal conclusion has been that they were a very early and complicated Z-wave device with some odd implementation details, and they clearly never opened up the details of their programming interface. I still have most of the Leviton dimmers from the same time period (VRI06 and VRMX1) and they are all still completely solid and reliable.
I don't like the Zooz button layout nearly as much (the vertical stack of Leviton buttons was easier for me to relate to possible scenes than the Zooz grid), but the Zooz controllers work reliably and hopefully I'll get used to them.. or fit suitable labels on the buttons. I might have preferred the button layout of the Inovelli button controller but gave up waiting for it.
The other thing I changed in the last few weeks is to add an External Antenna to my C-7, which has improved the mesh immensely. I have slightly wondered if this would help the VRCS4 behavior, but my feeling is their issue wasn't signal related, and I'm going to live with the Zooz replacements rather than going back to retest them.
Sorry this reply doesn't really answer any of your questions so much as share similar experiences.
