Very similar to my techniques except for a few things:
1) Don't use a chamois (shame in your post). They can be rough and trap dirt. I use an "Absorber". It's great. Synthetic chamois-like cloth. Much softer.
2) Don't use dish detergent! Let me repeat that: DON'T USE DISH DETERGENT!!! It is NOT good for the paint. There are additional chemicals in there that will have adverse effects on your finish. I use Meguiar's Gold Class wash. It's the best available in the local auto stores. If you want, you can find higher end washes online, but it's really not worth the extra cost for a daily driven car.
3) Mother's Clay Bar is ok, but nowhere near a normal clay. It's manufactured as a less aggressive clay for the average Joe. If you're serious about detailing, visit an online store and get a clay from there (I like Autogeek).
4) I usually wax by hand. I don't know why, but I just prefer it. I feel like I take more care getting even coats. I usually use a Meguiars wax just for the daily driver. Multiple coats work best.
Usually I get a decent result: