Get a bigger pan/oven?
How I would do it would be to lay out tin foil (ohgods, I just said "tin" foil.. jeez, how old am I? Aluminum foil!) and create a "drying pan" from it. I'd still do the hot coffee technique that I listed above (and possibly rip it prior to the coffee if you wanted that look).
Instead of the oven, I'd try a hair dryer on low (at first, until I got bored, impatient or figured out that high would not burn or ruin the paper) and try to dry it that way. If you're really patient, and your significant other doesn't mind, you could let it dry naturally, after mopping up the excess coffee. The trick is to have the aluminum foil "pan" be sealed at the edges/bottom so that you don't drip coffee through it. I'm not responsible for ruined carpets or tables.
I would probably experiment with this first before doing this on a real life poster sized map. Any chance you could get a blank sheet or two for practice?