Hi Caving_Fox
My club (York CC) had a long weekend in Clare a few years ago and it absolutely chucked it down on the first day, really heavy and relentless. Based on prior experience we had thought, incorrectly, that Faurnarooska was OK in wetter conditions, but after a very wet trudge up the fell in zero visibility (it is not easy to find) we were met with a wall of water cascading in only 10m into the cave (we returned later that week to realise that actually it probably is very flood prone further in due to low crawls in the stream). We thought our caving weekend was ruined.
The Cullauns too are very flood responsive indeed (1/2/5 being the most popular), as are several of the others you list including Doolin River Cave (St Catherines) and the Pollnegollum and Poulelva Pot system.
I am not really sure what is safe in wet weather; maybe contact SUI for their thoughts?
On a more positive note, we were astonished how quickly after the rain had stopped that the systems drained. The day after the heavy rain which totally wiped everything out, we completed the Pollnagollum/Poulelva exchange trip with no water issues other than a shower in the Poulelva pothole (note that the navigation from Poulelva to Pollnagollum is much more complex than the other way around due to a critical junction it is easy to miss going upstream; PM me for more details), and the day after we were doing Doolin River Cave, again low water even at the Fisherstreet Pot end. We were astonished , it was as if the rain had never happened. We didn't go to some of the mega-flood responsive ones (Coolaugh River Cave) as we suspected they would be unsafe.
I'm not saying this is always the case; hopefully someone more familiar can provide more details; just sharing our limited experience.
Therefore I'd certainly tread carefully while it is actually actively raining; not much vertical range and rapid run off into the caves... they probably flood quite badly. But be encouraged that if it does stop raining, you shouldn't have to wait more than a day before things start to become passable again.
Have a great trip!