A trip that is roughly a bit over a thousand miles on quiet roads for June and beginning of July somewhere in USA where the weather does not get too hot could be lots of places. But, most cycle routes of that length will include some busier roads.
When I did Pacific Coast from Astoria to San Fransisco, my GPS track said 863 miles. Starting in Portland OR instead of Astoria would push the mileage up a bit. But some of that route was on busier roads, so not sure if you would like that. When I did that I wrote up my observations at this post, but that trip was six years ago and this forum has changed software a few times, some of my photos at that site disappeared:
https://www.bikeforums.net/touring/9...l#post16933424
Adventure Cycling puts on trips (I know you are not interested in a guided trip) and they also sell maps for routes that they have researched.
https://www.adventurecycling.org/rou...route-network/ .
You also could look at their trips, and try to replicate one of their trips on your own if one of their trips sounded interesting. Some of their organized trips deviate from the maps that they sell, it would depend on which trip. It sounds like you have experience so you could certainly deviate from one of their routes.
Do not rule out parts of Canada. I did a five week trip in Canadian Maritimes last summer at about the same time. It was wetter than I wished, but it was enjoyable. There were a few busy roads, but I mostly stayed on quiet roads. I flew to Halifax Nova Scotia, did a loop out of there.
Side note on your bikes - Rohloff hubs in USA are extremely rare. You might want to bring a spare internal gear cable in case you needed to change cables on one of your bikes. And you are very unlikely to find a bike mechanic in USA that knows what a Rohoff hub is. But the internal gear cable is the only Rohloff specific part that I can think of that you should carry, other than the standard spares like tubes, brake pads, etc.
Have a great time.