Here's a good bit about testing baking power with a nice visual of what type of bubbles you should expect.
http://www.thekitchn.com/how-to-test-if-baking-soda-or-baking-powder-is-expired-tips-from-the-kitchn-111759

Have you changed your flour brand? Sometimes southern flour is softer than other parts of the US. Maybe try a King Arthur AP flour instead of Gold Medal.
And also check your baking power...not just for exp date, but a test bit in a glass of water.
And if you weight flour...be sure to use a chart that brands of flour.
Sometimes the gram weight can vary a lot from brand to brand.
http://cooking.stackexchange.com/questions/2915/standard-weight-conversions-for-converting-cups-of-flour-to-grams-of-flour
http://www.recipesource.com/misc/hints/flour-weights01.html

Keep in mind that for many cookie recipes, the cookies' height and chewiness benefit from some chilling before baking. I'm not sure where you moved from, but your kitchen in your new home could be warmer and more humid than your previous kitchen. If so, some pre-chilling of cookie dough might help a bit.

Check out your baking powder.

Check out your baking powder.

I suggest you get an oven thermometer to ensure that your oven is at the temperature intended for your various recipes.

Assuming you do this, you continue to have problems, and you have successfully executed these recipes when you lived elsewhere, my next guess would be that there is something about the local water that is making baking difficult. You may want to talk to your neighbors and experiment with bottled water to see if that makes a difference.

Good luck.

Not sure what the problem could be with your cookies, but do read your oven's manual. It will tell you how to recalibrate it. Do you have an oven thermometer? You'll neec one to see which way and by how much your oven is off.