Nice bike, Amy. MS 150 is totally doable in your timeframe.
Your back is likely hurting because...
1. Bike Fit. Get a professional bike fit. It'll be $100-$200, so if that is in your budget, do it. It will likely help by tweaking your bike and perhaps making some changes to the stem.
2. Your position: I bet you are scrunching your shoulders up to your ears when your ride. Relax your shoulders, keep your elbows slightly bent. #1 and #3 will help.
3. Core strength: If you are scrunching your shoulders up to your ears, you are not using your core to hold your body on the bike--you are leaning on your bars. Do Pilates or other core strengthening exercises regularly to correct this.
Enjoy your rides!