I was having some lower back and neck pain last week during and after my ride, so I raised my handlebars a bit (and to achieve more of a neutral hand position to eliminate hand numbness...still had a little of that too) to try and correct it. No pain in my lower back or neck, but I still had pain in the middle of my back. Does anyone have any suggestions? Do I need to move my seat forward or back? Rotate my hips back?

Thanks!

You can get lots of suggestions from folk on the inter-web who can't see you on your bike and have no idea of your level of fitness or a plethora or other relevant facts, that may not be too useful to you.

Instead: Have you been to an experienced fitter in you area?
Have you gone through any of the well established fitting systems yourself to evaluate base line positioning on your bike?

-Bandera

My LBS guy (where I bought the bike from) is really nice, but I'm not sure how experienced he is at fitting. I was having some numbness in my left hand, so I took it back up there and he moved the handlebars down and moved the seat back a bit to take some pressure off my hands, thus resulting in the neck and lower back pain. He told me I can take it back up there any time and put it on the trainer, so I might take him up on that.
Another issue might be that I usually don't stretch before I go out. I used to kayak and learned the hard way (i.e. throwing out my back) about not stretching. So, I know I need to do that regularly as well.

Sounds like you are on the right track, if you know that stretching is essential pre-kayak then pre-bike seems sensible. A bad back is a bad back and must be treated w/ respect regardless of the means of self propulsion.

Your LBS guy is working with you, good on that. Aches & pains are part of the process of adapting to cycling, and a consequence of doing it well.
A continuing dialogue with your fitter is in order, put miles/hours in there is no substitute.

-Bandera

PS
Can't hurt to research a well proven fitting system and go through all of the steps yourself.

Maybe reading this could help. https://www.bikefit.com/s-13-road-bikes.aspx
You can print it and take with you to the shop as well and make sure they cover all the details