God damn it... Look at the bottom, that's where it falls apart. I thought the overlap was because they're all a bit different (since it's real life and not a perfect geometry puzzle) but I'm now pretty sure it wouldn't work out even if they were all perfect. Gonna test it with CAD tomorrow afternoon, just went to bed and have a busy day so can't do it before that.
Here's the part in question:

Kinda disappointed in myself that I didn't see it until you pointed it out, it's usually so easy to notice when something off about nice geometry even when it's just a feeling at first.