OP, I take it when you say "Credit Card Camping", you mean staying indoors at hotels and the like, not actually camping. (Though I would love to see someone tour by actually taking a credit card camping tour
and set up tents inside motel rooms each night.
I looked over a couple sections of the Sierra Cascade Route, namely sections 1 and 2, from Sumas WA to Crater Lake. Yeah, it looks like you can do it for that length, but there will be those long stretches sans service like zzzz mentioned. And you'd probably have to book space far in advance, as the lodging options are either small, or in a touristy area, or both. So you would be "locked" into a schedule. Still, it would be safe to have a camping setup as back-up, just like zzzz plans to do.
I've done parts of the northern part of the Sierra Cascades, and it is definitely a beautiful route, but challenging.