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Your trip plan really hits a wall at the end. It is nearly 800 miles from LA to Grand Junction, which is way too much to try to do in one day. It's really too long under any circumstance, but trying to do it at the end of a massive trip like this is particularly dangerous.
The problem really stems from the fact that Chicago to LA is just too far to do in 3 days. Your other 2 days after Chicago are already at the very limit of how far you can safely, so you can't add more time to them to fix the issue.
There's a couple things you could do.
One, add a half day to your plans. Spending your last night on the road in Vegas would work out well.
The other is to trim your off-day in Chicago to about a half day, and get to Iowa City that night. Then push your other stops back to Julesburg CO, and Salina UT. That's really about the farthest you should consider driving on any of your legs, and even that really won't allow time for any extra stops beyond the very basics for fuel, food, and other quick breaks from the highway.