I've been working on a glass display box for a Nautilus model I have. I'm self-taught and prone to procrastination and second-guessing, which explains why it took me several months to do this pretty simple project. But, you can see photos of the semi-finished project at:
You said you will find another way to make the 45 degree joints. I've never built a case like that, but I think that a shooting board and hand plane would make short work of it. You can adjust a miter with shims, even a paper's thickness.
A friend of mine once told me something that I've taken to heart when it comes to projects: The best time to start a project is right after you finish it.
So far it's held true in every single thing that comes out of my workshop.
For the base, which probably won't straighten out like you're hoping, you can always just take some of the scrap oak and make some feet for your case. Even 1" feet with some nice curves will help. Also, it might help when you move it to another location. You can work to make sure your boards are flat to 1/1000", but it won't do you any good if the thing you're setting them on are wavy and warped. :-)
Did you use the same amount of finish on the top and bottom? If the number of coats is unequal, one side could adsorb more moisture than the other which will cause it to warp.
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