I was determined to use appropriate veneer for the cabinet’s door panels; viz. full width, reasonably thick (un-jointed 13″ [330mm] span, greater than 3/64″ [2mm] thick), Swietenia macrophylla mahogany as would have been used on the original doors. It proved a tough assignment.
Solid S. macrophylla was available (even up to 26″ wide!), but my current bandsaw only has a resawing capacity of about 10″, so that ruled out sawing my own veneers for the doors. I sourced three parcels of veneer from Australia, England and North America. The North American stuff was so thin it was almost transparent, the local stuff turned out to be the most hideous cut of coarse African Mahogany (actually Khaya spp.), but a small mill in England cut me some good thick stuff.
The gossamer-like veneers widely sold today present no difficulty in laying even for rank amateurs, but curls and thicker cuts of veneer – as employed in the eighteenth-century – often necessitate the use of veneer pins and profuse expletives to lay them successfully. Thomas Sheraton offered some sage words on the subject:
If the veneer be of a pliable kind it may be laid with a hammer, by first shrinking and tempering the veneer well, which must not be by water, but thin glue [size]. If the veneer be very cross and unpliable, as many curls of mahogany are, it is vain to attempt the hammer. A caul in this case is the surest and best method, though it be attended with considerably more trouble than the hammer. 
I “attempted the hammer” and succeeded in laying the veneers on both door panels. When dry, the panels were trimmed to size and fitted into the door frames behind the astragal mouldings (fig. 1). The panels are retained by 1/8″ thick cockbeading nailed around the door frame behind the panels.
The cabinet was set on the chest and centralised on the back edge. I mitred the separation moulding around the cabinet and then glued and nailed it in place (fig. 2).
 Thomas Sheraton, The Cabinet-Maker and Upholsterer’s Drawing-Book,
Ed. 3, revised, T. Bensley, London, 1802, p. 329.