In a few months, an IR video will tell you exactly where the heat is escaping... You want a big temperature differential to really show it.
Did they put a blower in your door to see how much/where you're leaking?
I still don't see how new, high-efficiency windows would cause your bill to go up??? Did you see them installed? Were they using ample foam sealant? Do you feel (hot) drafts near any windows?
When we had ours replaced, we had one of our sliding doors that had a virtual hurricane coming from one corner. They came out and basically re-installed it, and the draft is gone.
Our original ones leaked so much that you could feel a breeze by every window in the winter!