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While I personally would not do your route/itinerary due to the high daily mileage (for me), your route is doable but may not be super enjoyable if you are not a strong rider. Even then. I get the sense that you are on a time crunch, thus the high mileage. I personally find that the tour enjoyment starts to degenerate after the daily riding AVERAGE creeps above 60 miles per day. My sweet spot after 45 years of touring is around 54 miles per day but I like to stop and read the historical roadside signs, talk to locals, etc. Of course, preferences will vary for each person.
You don't say how experienced you are as a long-distance cyclist or how much you ride. Some of your days are a bit long, i.e., 15 days with 80+ miles. You average riding (not including rest days) day's mileage is almost 73 miles and doing that many miles or more day after day wears on you. I am assuming you are riding a road bike and not a mountain bike. Also, remember that the days are not quite as long as summer time and with DST kicking in, it still may be dark as late as 7:45am in case you are an early morning rider. Also, the first 5-6 days might be somewhat boring due to all the interstate riding.
Definitely consider breaking the long day @ 119 miles into two days as you might be into a headwind as possibly with the other days you are in west Texas. Check out WeatherSpark.com or WindHistory.com for wind direction info. If you are forecast to have a tailwind, then sure, crank it out, but it would suck having to do 119 miles into a still Texas headwind.
Since it appears your brother is going with you in the RV, you are not carrying your gear, correct? Just "day ride" stuff while riding. If not, your mileage is definitely on the high side unless you are a very strong rider. Is your brother on his own schedule or is he just following yours in case you get sick, have a mechanical, weather, etc. that slows you up by a day or three? What happens if the RV breaks down for a few days?
I get the sense that you (or your brother) might be on a time crunch, thus the high mileage. If not, I would highly suggest you lower your daily mileage so you have more time to stop and smell the wildflowers. If so, I understand the need for high miles and as I have said, the tour is doable but I hope you are a strong rider and you have no delays.
Finally, if you are looking for a riding buddy, I would suggest you do a posting on CrazyGuyonaBike, BikeForums.net, and the ACA's Forums/Classified.
Whatever you do, I do wish you and your brother a wonderful trip! Tailwinds, John