I did a lot of experimentation and tried a lot of different bottles. I'm extremely happy with the solution I have now.
I got a wide-mouth, 12-oz. Kleen Kanteen water bottle with the loop top:
And a collapsible beer can koozie:
Weight is 5.8 ounces with the koozie. That is about an ounce more than my previous mug, but overall I save weight in my kit because this bottle is truly a multi-use solution:
1. Coffee/tea brewing: The MSR Mugmate filter can be (barely) stuffed into it; so that's how I brew coffee.
2. I prefer stainless steel, BPA-free mugs over plastic, which leaches all sorts of stuff (not just BPA) when hot water is applied. But double-walled stainless steel mugs/bottles are heavy (~10 oz.). This single-wall bottle with koozie is a much lighter solution.
3. Obviously, it's also a daytime water bottle. I like carrying it in a side pocket and being able to put drink mixes like Perpetuem in it.
4. Can use it as a water scooper to fill my Platypus bottle in streams. (I sterilize it with Aquamira drops afterwards.)
5. Greatest thing of all, it's just the best HOT WATER BOTTLE for my feet at night! I was able to leave several ounces of chemical hand/toe warmers behind. Those hand/toe warmers are expensive and I hate sending them to the landfill. Now I just brew tea for dinner, take a few sips and use the rest to warm my feet. This bottle is completely leakproof. The koozie keeps it warm for about 6 hours. If I additionally wrap it a hat or gloves, it is still somewhat warm when I wake up.
6. Surprise discovery, it's a safety mirror! The inside of the bottle is made of an extremely bright, mirror-like material. So I leave my standard safety mirror at home now. More weight saved.