First, I am a full timer so the way I travel is most likely not the same as your situation. I like to limit myself to no more then 250 miles a day and I like to pull in to the new CG by about 3:30. Over the course of 6 months this year, I towed about 7200 miles.
In your case, the very first thing I would do is map out your travels so you know the total distance you are traveling in 6 weeks. I just asked Siri how far it is between L.A. and NYC and she replied it was about 2500 miles. So that's 5000 miles in total or about 120 miles per day on average - with no stops. Looking at it a different way - you could drive 360 miles and sit for 2 days, then repeat, etc.
I suspect you're going to be doing some very long days whether you want to or not.
If you take the same roads going and coming, then you may just decide to take your time 'going' and then do the return trip in fast mode. But if you're planning to drive some kind of loop, then you'll have to plan it out so you more or less average that 120 miles per day over the course of x days - OR factor in some long days.
Just my .02