F.W.I.W ....
How about installing a precast concrete bathroom facility. Costs about the same as a (really) nice car, vandal proof, and meets all current building/ADA codes. We've installed them in our parks with much success. Some models are very posh, too.
This doesn't resolve the situation for 'non-residents'. But, to temporarily circumvent the sticker restriction, is it possible to visit the Gilford clerk's office to change your primary residence to Gilford (maybe for a week or two), obtain the sticker, and then change your residence back? I don't think it costs anything to change your residence.