We are looking to make a 'practice' run this Spring, making a cross country trip for 6-8 weeks. It could very easily lead to a full-time period, depending on how it (and some work items) works out. ...
The Laundromat option will save you the most time. Not sure how much laundry you're talking about but you'll have multiple washers and dryers to use. Or find a place with the bigger machines. Wherever you're staying, ask the seasonals or annuals where the best place is to do laundry.