Like you, Nigel - I am a long way from any cup and ring rock art and know nothing about it. However, I have seen an awful lot of it coming on to the Portal and have often asked contributors if they have any theories about them. The answer is nearly always no. I like the way you have put your tentative case. It seems to me that we have a major enigma in British rock art and it does seem worthy of concentrated in-depth study. I understand that the rock art of northern Britain is similar to that of Galicia in Spain. Can we see other cultural links between the two areas ?
In response to your ideas:
The first question I would ask with regard to the gnomon idea is a simple one. Do such designs ever occur on north facing rock where the sun never shines? The second question is to ask if the same sort of design is ever found within structures - again where the sun cannot reach. If either were to be the case, then that would suggest that the gnomon idea is a non-starter.
Assuming that these designs are not purely decorative - ie art for art's sake - can we assume a ritual/funerary purpose?
Considering for a moment the possibibility of a non-ritual use - could they be direction indicators, maps (of communities or barrow cemeteries) or even star charts?
To me they suggest a language or numbering/tallying system. Has anyone systematically transcribed the designs and looked for similarities and differences? That would be the way to begin to decipher unknown hieroglyphs, pictographs or alphabets. Before anyone jumps on me from a great height - I am not suggesting that cups and rings are secret writings! I just point out that the discipline used to decipher ancient texts and modern codes might be useful. That is to catalogue all that you can and then assemble like with like and separate the dis-similars. Then you look for repetitions and patterns ie does the same symbol occur in the same sort of place in the same aspect? Does the surrounding natural and man-made landscape relate to that perceived similarity?
Probably the enormous library of rock art photos on TMA and the Portal should provide sufficient raw data to begin to compare designs and see if anything begins to emerge. I doubt if the study of individual examples will ever lead to an understanding.