The good thing about taking this cab to a jam was that I not only got to hear myself play through it - which was fine - but also got to sit in the room while another jammer played his Precision through it and then the house band bassist Gavin played first his double bass and then my Jazz through it. And they all sounded great, but particularly the last of those which maybe shouldn't surprise as I'd set the amp up to make a sound I liked from my bass and Gavin is a much better bass player than I am. Perfectly adequate volume for a jazz band in a small-to-medium size function room and all in all doing exactly the job I built it for, which is all I could ask. Plus it weighs a very manageable 7 or 8 kg, carries nicely, and if I say so myself looks pretty decent - I'm very happy!
Back at home, I did a side by side test with the 112 and I actually found it easier to get a sound I really liked out of the 1x8. It does appear to be, as Phil says, a pretty musical little speaker.
Advice for potential constructors? Go for it - this was really not difficult to build. I guess I think I know a little bit about woodworking but I'm certainly no expert, and any issues I did encounter were mostly the result of pressing ahead without double checking stuff, and were fixable. The total cost is going to depend on how you want to finish it and on what tools and materials you already have or need to buy, but I'm pretty certain it'll come in a lot less than you could buy something new with equivalent specs. Do ask any questions, there are no stupid ones - I really am no woodworking expert.
Thanks once again to Phil and other contributors for the design and the invaluable hints and tips I've picked up on the various cab design threads here.