Hi Wayne,
I have done the TA, NT, PC, & Katy Trail (among others). I personally think the NT is not very scenic between Fargo to around the Red Wing area. Since you have five months (you lucky dog!) to ride, I would probably ride to and do the entire Katy (end in Clinton, MO) and connect to the TransAm in Girard, KS. Then ride to Missoula, MT and switch to Great Parks Route. Now you can take in the great scenery of Glacier National Park and do a loop counter-clock-wise to Waterton National Park (in Canada so you need a passport) to Roosville, MT. After this, take the NT west to the end and then connect to the PC. Got it?
This above route is roughly 5,500 miles which should very doable in 5 months with plenty of stops for sightseeing.
I can't help between the PC and Joshua Tree but be sure to ride thru the Big Sur area (fantastic!). Maybe you could look into continue on to the end of the PC, ride over to the Sierra Cascades and up to closer to Joshua Tree?
Here is a link
http://www.bikely.com/maps/bike-path/Katy-Trail-to-TransAm-Connector-WB for a route that connects the Katy Trail to the TransAm in Girard. I haven't ridden this in about 3.5 years and have had conflicting notes as to whether there are convenience stores (CS) still open between Nevada, MO and Arma, KS other than Liberal, MO. If you want the GPS data for this route, email offline and I will get to you.
I really liked the variety of the TA route. I loved the "Big Sky" of eastern Montana and especially northwestern Washington on the NT. The coast is a classic also but definitely do it southbound. I didn't and wouldn't recommend it.
Sounds like you are in for a heck of a great trip!