Thank you both for the help. The lamination will be done with polyurethane, because pva sets far too fast, and it also gives a better result with the laminations (it makes them virtually invisible). I will try doing the slats with pva, on the basis that the cleanup will be easier in between all the slats, in the fiddly gaps etc. I was also hoping to put the finish on (or at least the stain) before I glue it together. Is that feasible? (Edit: actually read all of Mike 's answer this time - will apply the finish first).
Currently I am making some new clamps (
How to make your own wooden sash cramps) but I had an epiphany yesterday - I have enough clamps (for this job, at least) but they are not long enough, so I will try making some sort of extensions for them as well. It
might work. I'm thinking piece of wood with a hole at one end for the clamp head, and a right angled piece to hold on to the work, possibly with a mortice and tenon joint. It's all a voyage of discovery at this point.