The real cost killer on a cross-country drive is often accommodation, so here's something that doesn't always come up: consider mixing cheap motels with camping or staying with friends if you know anyone along the route. Camping can run you like $15-30 a night in many places, versus $50-80+ for a budget motel. Apps like iExit let you see what's available right off the highway so you're not scrambling at night. You could also look into staying slightly off major routes - sometimes small towns 20-30 minutes from the interstate have way cheaper lodging than places right on I-80 or I-40.
Food is your other big leakage. Grabbing meals at restaurants adds up fast, so hitting grocery stores for snacks, sandwiches, and breakfast stuff saves a ton. A cooler takes up minimal space and lets you make sandwiches in your car or at rest stops. And yeah, your route matters for fuel, but since your sedan's already pretty efficient, the bigger win is just not backtracking - driving a sensible straight-ish path beats chasing slightly cheaper gas 200 miles out of your way.
One thing worth thinking about: what's your actual timeline? If you're flexible and can take an extra day or two, you can aim for the cheapest gas stations rather than pushing 600 miles a day and needing pricier, convenient fuel. How fixed is your schedule for next summer?