re: Incense Box

Good morning, Martin - or whatever.
Yes, I always use solid wood.  Veneering and marquetry is a whole nuther rabbit hole of learning and tooling-up - either of which I cant afford right now.  Someday, probably.
I have tried to find Pawlonia here ( I know it is often used in Japan as a substitute for the old growth cedar they prefer).  Bauhaus (one of our Big Box stores of German lineage) used to have laminated sheets of it but they dont carry it anymore, apparantly.  I buy almost all my wood from suppliers to luthiers, because I know it will be reliably stable, and none of them carry Pawlonia.

I am familiar with the technique of the cloth, added for strength.  Alot more to do; will likely start doing that, eventually.  I havent ordered the Tonoco? powder yet, but do intend to.

I use Basswood because it is very similar to Pawlonia and Cedar, also, it is cheap, and luthier suppliers carry it.  Once you get down to 5mm or less, basswood can behave in a fashion that is not ideal due to the humidity here - until you get the sealer coats on.

Routing Basswood is problematic, almost sure to cause chipout/tearout to one degree or another on such thin stock, so I would do any cutting on a tablesaw, and that limits possibilities where curves are concerned.  I dont have hand-planes for those types of operations.
Here is my issue with cutting separate lips on tops and bottoms (that sorta sounds like a line from an ACDC song).  The many coats of lacquer need to be accounted for, and because I dont have that down to a predictable science yet, it is a guesswork.  The fit cannot be too tight, or too loose.  Either the register needs to be thinner + the lacquer, for a proper fit.  Or, the groove for the register needs to be thinner than the registers + lacquer X 2.  You understand?  My solution to this is to add the registers after all the lacquering is done, and keep them lacquer-free - whether in tops or bottoms.  The easy way out, in other words.  You know, I am basically teaching myself here, no mentor.

I will go and investigate Japanese joinery techniques for box making, looking for similar diagrams like the one you posted.  I know they often use rabbets, rather than miters.  Thanks for that info.

P.S. I am one of your Followers - over there at Pinterest.