Ah, yes you did mention that above. My apologies.
For measuring flatness/parallelism, the best would be to set it up on a large surface plate, but you may not have access to that.
Can you set up an indicator to run on one side to check the alignment to the other? If it isn't aligned, then you're probably going to need shim stock and tapping things around with a small plastic hammer to get it aligned. Once you get it where you want it, you should drill for dowel pins (tapered, usually) to enable disassembly/reassembly and to make sure they stay where you put them.
Or, using a smaller surface plate (or other surface flat enough by your own standards) you can print it and scrape it flat.
There are a few ideas here, but I'm just kinda throwing them out there because I can't quite visualize exactly how you need to align things.