I've had the same problem with titanium, including the mini-solo kit's cup. (By the way, I always found the cup to be too small for much of anything except measuring or using as a bowl for morning oatmeal; I'd prepare my tea in the taller pot - and it would be cool by the time I drank it.)

My solution was to quit drinking hot beverages, and just drink water. That made the Trek 700 pot an adequate kitchen. It also saved the weight of the tea bags and cocoa mix.

About a year ago, I started moving away from titanium cookware; I missed my tea. I decided to "spend" a half pound of weight and begin using a JetBoil stove. It was heavier on weekends, but fuel efficiency made it break-even for longer trips (one fuel cylinder instead of two.) I can have a hot beverage, and drink from the plastic cup, or I can have a full pot of tea; the plastic lid for the pot eliminates contact between lips and metal, so it's possible to drink while it's still warm. The pot cozy keeps the tea hot all through the meal. My usual routine is to heat a full pot of water, using some to make oatmeal in the cup and the rest to make tea in the pot. For evening meals, I usually cook a freezed-dried meal in the pot and have cocoa for dessert. However, I suppose I could cook the food in the bag, eat from the bag (or spoon out a small cupful at a time), and have another pot of tea. (I don't like cooking in the bag because it leaves me with a messy, wet piece of trash.)

Another option, if you're willing to carry the 10 or so ounces, is the GSI Pinnacle cook set. It has an aluminum pot and lid, a large bowl (with cozy) that converts to sippy-cup mode if you put the pot lid on it, and collapsible spoon; everything stores in a coated-nylon stuff sack that doubles as a sink. As a bonus, a small canister stove and fuel canister store inside. It's also a lot cheaper than titanium.

If every ounce matters, titanium is the way to go. If you're willing to carry a little weight, the aluminum options make more sense.