I wouldn't recommend a hammock for the Trans America and would guess that it is even less suitable for the WE. I know that we didn't see trees for quite a while at times. I highly recommend a freestanding tent that can be pitched on concrete. We often found it handy to pitch the tent on the concrete pads under pavilions in city parks. In hot weather this allowed us to leave the fly off of the tent and therefore have better ventilation. In wet weather it allowed us to have a dry tent in the morning.
Our route was different, we did a West - East Trans America starting June 11th. I used what was supposed to be a 30 degree bag and it was just OK. I was a bit chilly a couple times, but never really cold.
Regarding the Western Express. I haven't done it but will say that you will be missing a lot of the best parts of the Trans America if you do the WE. That is just my opinion, but while I enjoyed the arid areas there were enough of them on the TA.
How long do you plan to take for the trip? At a somewhat normal pace you will hit Pueblo in about a month or so and you will be in the heat of the desert for the month of July and maybe a week or two of August. It was hot enough for me on the Trans America (We had 100 F days a lot of the time). I am not sure I would want to deal with much hotter weather. I also would hate to miss Yellowstone, Lolo Pass, the Cascades, etc. in favor of the desert on the WE. I know we were SO happy to see trees when we got out of arid areas. The variety of terrain is a big advantage of the TA and you will have less of that with the WE.
Don't let me sway you too much though, I know folks who love riding in the desert and there are some really pretty places on the WE.