The route in the link provided is just a basic outline of what direction I am thinking of going. I'd of course love to visit as many places along the way.
Whilst I was on my previous trip I enjoyed driving along the smaller, less traveled roads. It was nice to be able to pull up to take pictures and not have another person for miles. I also found it more interesting visiting smaller towns than staying in the big cities. It was great to see the small local stores and meet real Americans who have stories to tell.
I'd prefer to do most of the trip on the smaller roads but I'm guessing to get it all in, in the timeframe I've specified I would need to use interstates?

I'm pretty mobile when it comes to my disability, I use arm crutches and a wheelchair to get around. I used my arm crutches a lot more than my wheelchair when I was in the US previously. Out of the national parks that I went to there was only one that I didn't enjoy as much, which was Joshua Tree NP. This is due to the fact that it's a hiking park and I'm unable to do that, however there were places where I could pull over and take pictures. The Grand Canyon was amazing as they allow anyone who has a disabled placard to drive along the tour road, so I was able to get to all the vantage points and see it all.

The reason behind having a trip just one way across the country was that I thought it would add a significant amount of time to the trip so I'd have to cut out things from the trip to ensure that I can get back across to the initial airport.

Thanks again for your help and I welcome more feedback.