I think I'd either seen this one before or at least had a Lordenshaw stone mentioned to me, but the Lordenshaw stone does need a little, tint leap of faith to accept that there's bone fide rock art on the same stone. The Eel Hill one is indisputable!
The thing with bullauns is that in Ireland they were in use throughout the early Christian period and some are in definite Iron Age contexts. One or two are in Late Bronze Age contexts. There are a few in no context, which look positively Neolithic.
In Ireland, at least, bullauns are the only link from the Neolithic through to the present day (many are still used for 'wart wells' and as part of Catholic ceremonies. It's not hard to see how the Catholics turned to worshipping at Mass Rocks during penal times, because the branch of Celtic Christianity they originated from had been doing it for the previous 1200 years. Some bullauns have been in use for over 2000 years and some possibly over 4000 years. That's an amazing thought.
I'm not saying every single one to be found in Ireland is from the Neolithic, just that a significant number are. There are around 1500 or so bullauns across Ireland and would say that upto 300 could be old ones, maybe more. There are also going to be a lot more buried under the peat that formed around 2000 bce, which are obviously 'old'.
The upshot of all this recent activity is that the archaeos have not allowed themselves to consider such a long time frame for bullaun use. Even when confronted with French examples in a Megalithic context they say nothing.