Greybeard, I'm struggling a little to understand what you are thinking of probably cos I'm not a 'wood' man but I think you are wanting a vertical spindle with basicly a 30mm saw mounted on that same spindle?
how about a 10mm longseries cutter which could have plenty of shank onto which the saw assembly could be mounted it would need an appropiate
hole through the saw and a bespoke mandrel type of thing to lock onto the 10mm cutter shank and drive the saw.
you will comprimise on the cutter ridgity... you need to hold on that shank firmly...but if only in wood... sounds possible
you were probably already reckoning on passing the saw right round the profile?therefore only needing to saw just over halfway through the stock.
nice to see you're in the UK, I'm in Dorset.