Could use some help with a cabinet that isn't square!

As a newer woodworker, I'm looking for some sage-like advice.

I'm working on a cabinet that's going to have four shelves on the bottom and a few small drawers at the top. It's nothing too fancy, but I wanted to use dados for the shelves. Well, this was my first time cutting dados with a router, and it was frustratingly difficult to get them lined up correctly on both sides of the cabinet.

Ultimately, I knew some of the dados were slightly imperfect, but when I dry assembled the cabinet, everything was able to fit. So last night, I got everything lined up, clamped, and glued up. It actually came together okay, but the problem I'm now facing is that it's far from square. This has manifested in both the feet, which have a decent wobble to them, as well as in the drawer slide installation. (The drawers are not sitting flat when placed on shims on the top shelf, which leads me to believe the boards are somewhat twisted.)

My questions are as follows:

a) Is this a problem I could fix in any way?

b) I'm half tempted to disassemble by cutting the shelves out flush at the joint, sanding clean, then using something like pocket screws where I can ensure a square alignment. (I don't have the same aversion to pocket screws that most do. Haha.) I assume I would lose about 1/8 to a 1/16 of an inch from the cuts, but that would be fine. The dados would also be filled in due to the remaining shelves.

Is this something that could be done, and if so, what's the best way to get a flush cut at the joint?

Thanks in advance for any input. I feel like I've learned a lot from this project and I'm hoping to be able to clean it up a bit.