The last NAOC event is the Sprint on Sunday at the Dartmouth campus.
I just talked to someone at Dartmouth's Zimmerman Fitness Center about showers. They said: anyone can use the Zimmerman facility (even if you're not a student, staff, or alum), and it's $10 for a day pass.
Just FYI...and please post here if you know of cheaper options.
Those who are camping have access to the showers in the campground.
The fitness center may be willing to offer a special day pass for orienteers, if somebody has time to pursue making a deal with them. We had good luck working with the Miami University Recreation Center when we did meets there.
When I organized IS/IC Champs in 2012, I contacted a YMCA in between the Sunday event site and the airport, and worked out a group deal, and I just paid a flat fee for everyone, then put shower tickets in each packet.
I found this one listed on an AT hiking website:
Richard W. Black Recreation Center* – Laundry and
showers. $3 showers, $2 laundry – includes box of soap,
towel, and detergent, pay at the front desk. Also accepts
pack storage during business hours. Lebanon Street
between the high school and the Co-op grocery store in
Except it looks like they may not be open on Sunday :-(