Student wrote:
....
...story of complicated glue snipped for brevity...

My first question: Do you guys have situations like this, and how do
you go about assembling the case.

Everybody does on occasion, of course.

Couple of things--use a glue w/ a longer open time. TB III is over I or
II, there are specifics for the purpose as well readily available.

Secondly, the idea of gluing one end and then the other is often very
appropriate. To do the clamp up, the only thing I'd have probably done
differently would be to have used the other side w/o the glue to aid in
the square-up process in the first step. If I thought it were too many
at once, I'd even have only done half, say, of the first side the first
time.

Lastly, experience will help. You'll learn and get more adept. Also,
making sure all clamps are preset to rough size, everything's handy, dry
fitting, etc., etc., are steps to take.

I also had a problem with the veneer chipping off the plywood for
every crosscut - miter saw, table saw, circ saw, all the same.
....

Mostly blade type and quality then would be the question. A blade
specifically designed for ply will cut very cleanly.

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