Searching for a firm to do the cutting for me, I read in MEW 291, the article by Mark Noel on various cutting techniques. He recommended a company in Nantwich that had done some work for him with good results. I went to the web site referenced at the end of the article, only to find that it is a similarly named company but in Lyme Regis, Dorset. A Google search soon found the correct address:
Precision Waterjet Ltd
I have emailed them with my request and await their reply. Incidentally, I approached a local(ish) firm in Sheffield, but they weren't interested, preferring, quite reasonably, to concentrate on industrial size orders.
I still have in my arsenal, the kind offers of assistance from Adam and Shaun above, of course. I'll wait to see the response from Precision Waterjet.
As an aside, I've also ordered a piece of A4-size clear acrylic to use as a base instead of wood, intending to place a mirror underneath that to further enhance the view of the workings. At least, that's the idea. I'll see what it looks like when (if) it's ever finished.
John