I have read and been inspired! I am about to get a selection of veneer from cardsofwood, who appear to be very helpful. Reading their website there are two thicknesses as DSiemens (how formal!) says, but the 0.016 thickness is paper or felt-backed (I think). Is this the material you tried?
My plan, fwiw, is to get assorted timbers in postcard size (0.025) and a pale timber in paper size (0.016) and they have offered some samples of other constructions not seen on the website. I will happily relate what I get and find - and do with it.
Harking back a little, and at the risk of being nationalist, French polish and French polishing are alive and well both in Britain and Australia, and many varieties of the mixed polish are available, as well as the flakes. My wife is a furniture restorer and we have several pounds of the flakes, and I have always used Button Polish (the thinnest french polish) as a fixer and ready-release holding glue for assembly or adjustability.
Off to order veneers. It has just occurred to me that these are intended for printing (different types for inkjet and laser) so printing or engraving deck planks with a laser might be convincing?
regards
andrew