Dear Scott Di Lalla,
Yes! quality of your poster will desrease, when you increase the 72 dpi to 300. Remember the rule, if you are designing any poster or document size for printing, at 1st your prefereces should be adjust on 300dpi or higher in Adobe.
You have done lot of work in poster with 72dpi, then the final solution is to ask prinitng press related person about to get solution. May be he can help you out according to his machine adjustment.
One more thing, make another copy of your poster and apply 300dpi on that. If you feel your poster is still ok, then you can carry your work. I also have faced this problem like you and did experiments with dpi.
All the best
takecare
Viqar Amjad