In case someone lands here looking for Z-Wave or OpenZWave integrations troubles:
My Z-Wave integration continued being unstable as reported above, so I decided to migrate to OpenZWave (Beta) following this guide. I had some trouble getting OpenZWave to work, but waiting it out seemed to solve the troubles.
However, I soon discovered that my OpenZWave integration became unresponsive. It seemed that Node 3 (a Namron Z-Wave dimmer) was flooding the Z-Wave network (log). Excluding the node and re-including it solved the problem - for a while. New flooding occurred after some time. Excluding the device, factory resetting it and re-including did not help. I then replaced it with a new dimmer of the same type and the OpenZWave integration and the Z-Wave network have been well-behaved since then.
It seems, therefore, that my Z-Wave network troubles were caused by a node that failed. The troubles started after a power failure in my neighbourhood, so I’m speculating that the power failure fried my dimmer (a bit), so that it flooded, and effectively jammed, the Z-Wave network while otherwise working well (local control was no problem).