So I've mapped out this much so far. There's still some flexibility, especially after AC. Take a look at the map and stop list:

https://gyazo.com/61e469b063ec169fd2692249a64b3ad1

July 3rd (Early Morning) - Depart Bremerton, WA
July 3rd - Rest stop in MT (Probably around Bozeman)
July 4th - Fargo, ND
July 5th - Council Bluffs, IA
July 6th - Watson, IL
July 7th - Columbus, OH
July 9th to 12th - Pittsburgh, PA
July 13th (Early Morning) - Depart Pittsburgh, PA
July 13th - Troutman, NC
July 15th - Orlando, FL
July 17th - Montgomery, AL
July 19th - Fayetteville, AR
July 21st - Rest stop in NM (Probably around Albuquerque)
July 22nd - Oxnard, CA
July 24th - Lake Tahoe/Carson City, NV
July 26th - Rest stop in OR (Probably around Grants Pass)
July 27th - Arrive home in Bremerton, WA