I work within defined limits for each feature. The thickness of the finished neck (fingerboard, spruce core and veneer covering) at the first fret is under 19mm. The thickness at the joint to the bowl is under 29mm. These are measurements for large lutes. I think that necks that are thicker will be uncomfortable. If thinner, the structural integrity will be threatened. Naturally this doesn't suit all lutenist. But I have found that compromise can be achieved by thoughtfully shaping the neck's contour.
I have never found it easy to apply veneer to the back of a lute neck. There are so many steps that are necessary to assure a good result. Perhaps I make it more difficult than it need be. I bandsaw my own veneer from 3 inch wide ebony boards that are sold as fingerboard stock for bass guitars. I finish the rough sawn pieces to a thickness of 1mm or a little less and bend them over a hot pipe using shaped cauls to ease the ebony into the proper curve.
Since the fingerboard stock is narrower than most lute necks it is necessary to use multiple pieces. I glue each on separately. Here the center piece is strapped down with elastic tape while the glue dries.