For whatever it's worth, I do not agree with lowering your bars, Elk.
The Jamis is a touring bike, not a racing bike. I think doing this will open yet another can of worms and compound your problems even further.

Ideally, a good LBS could help you with dialing in your bike fit. Please consider it.
But in the meantime....

The new picture looks good to me, and I hope the shims are helping you brake reach problem that you started out with. I love your description of your Jamis as a little Morgan horse- it looks just like one!!

I see that you have your saddle all the way back- that's good for now and will help keep your weight off your hands. But I think you have your bars tilted upwards too much. A good starting place is to have the tops of the bars be somewhere near level.
If the new bars feel too cramped and narrow, they could well be causing your hand pain, so possibly just put your old comfier bars back on? You wanted to get rid of the bar padding anyway, so....
On the old pictures, it almost looks to me that your leg is straightening out too straight on the pedal downstroke. If your leg straightens all the way when pedaling, then you should lower your seat a bit until your leg 'almost' straightens. Another indication of a too high seat setting is if you find your hips are rocking from side to side as you pedal. Ideally your hips should be relatively still while pedaling.

One thing we tend to do while riding touring bikes is to sit up straight and straighten our arms and hold ourselves up by leaning on our hands. Then we just let our stomachs sag down too and add more to the weight on our hands. Yes this can cause significant wrist/hand/shoulder pain. You can fix this without lowering your bars by breaking the sagging-back straight-arm habit posture. Concentrate on tipping your pelvis (by tipping your tailbone DOWN and your pubic bone UP) and curving your lower back more. (this will have added benefits of less pressure on your girly parts) As TxDoc noted, once your lower back is more curved (actually just less saggy) you can start training your core stomach muscles to hold you up instead of your weight on your hands.
I know this because I worked on correcting this posture habit in myself when riding my Rivendell touring bike with the bars the same height as the saddle. It really works if you keep reminding your body as you ride. That's my opinion based on my own experience on two touring geometry road bikes,
Remember, your bike is not a chair. Don't sit on it like you were just watching tv. Float over your bike and be one with it. You are essentially walking and moving inside a marvelous machine.