I know that you said that Thumper tenses up when you shorten your reins, and that riding with your hands in your lap actually helps you, but I've been there too. I think you should try to shorten your reins up a bit, but instead of having them too far back, try to put them forward a bit. It should have the same result, but will look much neater, and eventually will teach him that just because you have a short rein, doesn't mean you will tear on his mouth. Unfortunatley, this is a common problem with lesson horses. If you get him to relax with a shorter rein, you can eventually work on bending and working him onto the bit.
I think you look pretty good, and you and Thumper are a good pair. The no-stirrup work is defiantley a good idea to help you with your chair seat. Another way to fix that, is to shorten your stirrups up a hole or two. It may be uncomfortable, but it will strengthen your leg muscles, and when you do go back to a longer stirrup length, you will be able to hold your legs back in the proper position. Other than that, bend your elbows a bit.
On the great side, it's nice to see that you are sitting up tall, and looking where you are going, instead of down at the horse.
You guys are a cute pair!
~Kait & Mark~