I don't want to criticize your efforts, but it is best to use Plywood when wrapping inside mitered corners.
Solid wood when wrapped inside mitered corners will move enough to open the joints. This may take several years. It can happen very gradually or all at once.
The bottom can be loose fitted inside a dado allowing 1/8" movement from side to side. The bottom does not need any glue. Leave loose.
A solid top, if rabbeted into a mitered box like yours should have a 1/16" space on all 4 sides. This will allow for any movement. It should not be glued to to the sides.
That's why most tops are set on the top of the piece and not inside the piece.
I think you are too far along to change. You've worked hard for a good tight fit. If you glue the piece up as shown, it will be interesting to see how long it goes before you see a crack. It can wake you in the middle of the night, sounding like a gun shot or it can happen so slowly over time, you never detected the change. Good luck as you complete your project.
If you don't have time to do it right the first time, when will you have time to do it over?