Wont' any glue that seeps through create finishing issues, especially on such a thin veneer? It will be difficult to sand the glue off without risking sanding through the veneer and since there is a hole that the glue seeped through, it seems like the glue filling the holes will repel any finish you apply?
I have only used hot hide glue to hammer veneer (other than contact cement for laminates) and HHG is much easier to deal with excess glue squeeze out. In fact you actually apply the glue to both sides of veneer as you hammer it down and then clean off any glue left on the surface with water. HHG also does not suffer from issues with creep. HHG is a whole rabbit hole that you may not want to go down for one project but now that I have the gear to do it, is how I would do a small project like that.
The rule of thumb is to apply veneer to both sides but I only applied it to one side of this project. The "box" was made with HD 1/2" maple veneered plywood. The biggest problems that I had were getting the veneer to lay down smoothly on the inside of the circle and in places on the surface where there was figure in the veneer on the face. In a few spots, the figured areas wanted to warp away and I had to apply a hot iron and a wet rag to reactivate the hide glue and either rehammer it down or clamp it down with a caul (wrapped with packing tape and waxed).
--Nathan, TX. Hire the lazy man. He may not do as much work but that's because he will find a better way.
