How to make more than one good cup of coffee with a moka pot?
America's Test Kitchen recently tested Moka Pots. In the video, they specifically say to pour all of the coffee immediately when it's done brewing. They don't mention a metallic taste, but they do say that not leaving the coffee in the pot is important for flavor, and that it was equally true for all of the models they tested. So for your purposes, I would recommend that you use a good small thermos or travel coffee mug, and pour your second cup into that immediately upon brewing.

For what it's worth (since I was looking at ATK equipment reviews anyway), this one won their top recommendation for travel mugs: