Ok,
I've gotten a lot of really good information and I thank you all for taking the time to respond. Now, let me see if I understand all of this...
1. I need a bike fit, it's the only way I'm gonna get this really straightened out.
2. I possibly need a new stem that is shorter but still steep?
3. I could try rotating the bars up just to see if that would solve the problem.
4. I possibly need a new handlebar that is perhaps not quite as wide and isn't as "big" as the one I have now (ie I think by more shallow drops that you mean that the bars themselves curve too far forward thus making them harder for me to reach)
5. Now, the purpose of shims is to bring the actual levers closer to the bar, right?
Okay, boy, writing that out helped it make more sense. I'm gonna call that place that was mentioned and see if I can schedule a fit. I'm hoping that my LBS didn't actually sell me a bike just for the heck of it. When he sold it to me, he said it was a good size for me and it did feel good at first, but since I've been riding it on the trainer, it has been bugging me. So hopefully it's not totally wrong because I absolutely cannot afford another one.
So anyway, I appreciate all the advice and I'll keep you all posted...if I get her all fixed up I'll take some pics and show you.
Have a great day,
Gray