a trip to the "west" to raft would be much better if done closer to peak runoff. like late may or early june.
i have plenty of experience with shoshone, it is close and is runnable all summer. but, it is very short, you can't park a trailer at the put in, if by yourself the put in is a pain, and you have the interstate within 100 yards the entire way. it is a scenic canyon, and if you have never seen it you should run it, but i would not drive any great distance just to do it.
go hit cross mountain if you have the skills, that is a good run!