I have a HS3548 laced to a 20" rim from ebikes.ca. It has a Pirelli moped tire on it, and I've installed this on my TerraTrike Cruiser.
TIRES:
I live in Albuquerque, which has some very steep hills and some nasty thorns that have 1/4 inch needles. After messing with regular tubes, the Pirelli has been such a night and day difference. The tire keeps the same air pressure for months, and even after running over glass and metal objects in the road (we have bike lanes here but they get filled with all the debris from the road) they still haven't punctured or been cut. I have 20" tires on all 3 wheels, but only the rear wheel is running the Pirelli. I think the rims on the front tires may be too thin for the moped tire, so I'm planning on buying wider rims for the front wheels and running either Pirelli or Shinko tires (which are also a moped tire that I'm running on my 20" front wheel of my A2B metro). The Shinko tires are also DOT rated and seem to be very high quality as well. Plus they are a lot cheaper than the Pirelli tires.
MOTOR:
I'm running a HS3548, I'm a big guy, and I tow a trailer I built that my wife rides, which also has pedals so she can contribute to the ride. We have some very steep hills here (I live in the Rocky Mountains), and the 3548 has been able to keep up pretty well. If I was going on a longer trip, I would buy a Crown TC-80 or TC-100 and lace it to a 20" rim that can handle the Pirelli moped tire. The problem with the Cromotor is that it may not fit in the dropouts without stretching, and I personally wouldn't want to ride across the country on a frame that I've stretched out. These Crown motors from ebikes.ca come with a temp sensor that plugs into a Cycle Analyst. This is great because if the motor becomes overheated on the hills the CA will automagically back off power so you don't burn out your motor. With this safety feature you might even be fine with a 3548 motor, but the Crown motor would give you more reliability that comes with a larger motor. Either way, put a temp sensor in the motor if you don't buy one from ebikes.ca that already has one installed. The mid-drive setups are interesting, but on a cross-country trip I'd prefer the simplicity of a DD hub motor.
COMPUTER:
I have the HobbyKing version of the WattsUp meter that cost $19, but just recently switched over to the CAv3. The CA is such a huge improvement over any other type of meter because of its ability to limit your power to a certain wattage or even limit your speed. You can also set cruise control on there and monitor the temperature, as I mentioned above. The only regret I have is not buying a CA earlier.
BATTERY:
I am running 48V 24Ah of Nanotech Lipos. I charge with a Thunder 1220. This lets me keep my batteries wired up together so that when I charge I can charge at 12S and use one charger, one power supply, which means only one plug. The lipos are nice because they are cheap and relatively easy to buy from HobbyKing. I am fairly pleased with this setup, but I've been considering cellman (em3ev) batteries for one of my other bikes. The cellman batteries are nice because they're not lipo, so have a safer chemistry, and they come with a good BMS built into them. If you're going to have a trailer, I'd buy as much battery as you can afford. Two 48V 20Ah packs should be fine, but a third wouldn't be bad loaded at the bottom of your trailer. 48V should work well for you, since this will give you a top speed close to 30mph, which you won't be doing if you are trying to get good range out of each charge.
TERRAIN/POWER USAGE:
Your power usage really goes up when you start going uphill. I cruise at around 150 watts on the flat at 10mph towing the trailer. When I go up a hill it can spike up to 1400W on the really steep parts. Like dogman said, you'll reap the rewards on the way down the other side of the hill/mountain, and will give your motor a chance to cool off. Again, I'd get a CA3 and install a temp sensor in whatever motor you buy so you don't get anywhere near damaging your motor. Also, as your speed increases so does your power usage. When you ride around testing your rig you can get a better feel for the speed you are comfortable with.
GEARING:
I have 3 speeds on the front and I think 7 on the rear. I honestly never shift into a different gear since I maintain the same speed the whole time. The motor helps me get started, so I don't need to start out in a different gear than I use when cruising. Getting everything tuned properly and clean will help greatly with reliability... cleanliness and proper tuning have kept me from having many issues even with cheaper derailleurs.
TRIKE:
I've seen lots of KMX builds on here. I bought the TerraTrike because I got a really good deal on it, but I'm happy with it so far. It even has enough room for me to install my battery pack behind the seat, right up against the frame, so the balance is great. I also added a rear rack that I use for my waterproof Ortlieb panniers. These things are great and are easy to remove from the bike, yet stay on when you want them to. I'd say go try out some different trikes to see what feels comfortable to you, as well as keeping in mind compatibility with your build plans.
I've driven from Albuquerque to Kansas City many times and have spent lots of time in KC. It's a nice city, and your northerly route to Seattle should make for a fun trip.