Sounds like the wrong printer if they are going to be that fiddly. If you send them a 24 x 24" document and it is a hair off, are you telling me they cannot correct the image? Feh!

Mike's suggestion is the best way to provide a file for printing.

EDIT: Let me clarify that, because I'm assuming you know how the interface works, you may not

having upped the page size by 312.5% export at 96dpi

then you will have the right size image for the printer at 300dpi
Why not set the page size to the exact size, and export at 300dpi? This is what I have always done and I have never had a problem.

You are essentially creating a file that is 7200 x 7200.