OK, a few tips, partly echoing others here....
Touring is not necessarily about gunning across the country at top speed. It
can be about that, and while it is not my preference I don't see a problem with it.
However, I would say that if your reason to tour is to see a handful of specific attractions that are huge distances apart (e.g. "I want to see the Grand Canyon and Nashville on the same trip,") a bicycle probably isn't really the way to go. Cycle touring is about the challenge and/or the ability to really soak up the countryside, rather than "getting somewhere fast."
Also, you should realize that a solo tour is a very challenging endeavor, and if you haven't done it before and aim to ride at a high speed from the get-go, you could very easily burn out in the first week or two. Happens all the time, in fact.
Ergo, I highly recommend you ease into it and learn your limits before mentally committing to a huge tour. E.g. figure out a possible gear setup, and go on tour for a long weekend or a full week. Start with a mellower pace and see how you feel after 2-3 days of riding and camping. From there, you can get a much more realistic idea of a likely touring pace, as well as make adjustments to your setup.
If you still want to do the super-fast touring, your best bet is something like PacTOUR, which is run by a couple that were top RAAM competitors. They do a variety of tours; as an example, they do a van-supported Northern transcontinental tour, 30 days, 3500 miles, average of 116 miles a day. The riders are generally in a paceline on diamond-frame bikes and ride at 16-20mph. They do shorter tours as well, at similar speeds and distances. All are pretty much guaranteed to kick your ass.
As a contrast, Adventure Cycling does its unsupported southern tier route of 3100 miles in
60 days, including 9 rest days.
As to recumbent vs diamond frame, IMO it's pretty much a personal preference. Plenty of people use diamond-frame bikes and go around the world at a pace they like.
I'd say you should reconsider whether your goals are truly best suited by a bicycle tour, and figure it out from there.