Re: What would you do?
Try pumping in the morning at home: get up before DD does, pump some, then feed her. Start slowly so you're not shorting her too much, she'll nurse more to help convince your body to make more milk. I don't know that it'll let you get 2 feedings instead of 1 at pumping sessions at work, but it'll still help you get extra for the freezer.
Also, if you actually have something close to 1 hour with her on your lunch break, can you nurse her twice (doesn't work if most of your lunch break is tied up in travel time)? Once right away when you get there, and once right before you leave? Then you have more milk in her without having to pump more.