This is a cool idea, one of your biggest challenges will be that you’ll have to modify your GF’s case, which will completely house your warranty. I think you’re right about needing to vent the vacuum line outside, smoke and fumes need to be filtered or vented.
In all I might think that a properly jigged setup where you set the mat against reference physical jigs might solve your alignment problem without resorting to a far more complicated vacuum setup, but that’s up to you to decide.
Here’s the type of 2-sided jig I might consider if I were you:
https://community.glowforge.com/t/alignment-of-irregular-objects-coasters/16116