Reading through your post and Lifey's response, it is clear that your major hang-up on this trip (so far) is the cost of the hire car. And YES, being under 25 - even with a good driving record - can easily cause the cost of that rental to double. That is because car hire firms don't know, or care, about you. They work from actuarial tables that clearly show that drivers 24 and younger have and cause far more accidents than more mature drivers. By the way, they were the first to notice and act on this rather stark change in behavioral pattern at around age 24-25. More recent neurological research has shown that the human brain does not fully develop until that age and that risk aversion is one of the last bits to mature. So... as Lifey noted, you may be able to avoid the underage driver fee by going through a European consolidator, rather than dealing with the hire firms directly. A couple that you should check are Rentalcars.com and Europcar.
Other ways to save (although not as much) include hiring the car from a location other than the airport. I have often been able to save 20% or more by renting a car from a different location/franchise of the same company and all I have to do is take a short cab/bus/underground ride to get there. Often enough, you can still return the car to the airport location for no additional charge.
Thirdly, consider using somewhere other than JFK as your gateway city. If you do a complete loop, returning to the same city you start from (in the U.S.), then it doesn't matter where that city is as long as it is somewhere on your loop route. I'm guessing that every city on your list of 'targets' has direct flights from the U.K. except Omaha. The point is that New York has some of the highest prices for everything, including car hires, and you very well might be able to do quite a bit better renting in another city. Remember, it's the total cost of airfare and car hire that matters, and that is not necessarily the same thing as finding the cheapest flight and then finding the cheapest car hire wherever that flight dumps you off. Finally, consider hiring the car for slightly less than the full duration of your trip. If you land in/depart from a major city such as New York or Washington and plan to spend some number of days in that city before setting off on your RoadTrip, you are probably better off without a car for those first few days. Driving in big cities is a pain and parking is atrociously expensive. Plan on using public transportation instead.
Finally, Lifey is absolutely correct that if you are planning on having people join you for portions of this trip, and especially if you are expecting them to contribute to paying for a portion thereof, then this is their trip as much as it is yours and you need to get their buy-in on all aspects of the portion for which they'll be joining you. A good starting place for a discussion that will make sure that you are all on the same page is this quiz.
AZBuck