What "all-in-one" single serving tea device(s) are sturdy, make "teapot quality" loose leaf tea, and are two pieces or less?
Are you overthinking this? A small teapot, sized for one person, would meet your criteria, wouldn't it? Unless you count the infusion basket separate from the teapot itself, you just have a teapot to rinse out (no scrubbing needed) and a mug to wash. 

This is mine:


It holds around 20oz of water, so I can fill the pot, steep for a few minutes, then lift out the infuser basket and dump the leaves. You can easily do this in a breakroom or kitchenette area of an office, and then take the teapot back to your desk and voila, 3-4 cups of tea with one trip to the breakroom. Mine's made of cast iron and easily keeps the tea warm longer than it takes me to drink it. When you're all done, rinse out the teapot (cast iron won't need much more than a brief rinse) and wash your mug in the sink. 

Based on my tea this afternoon (admittedly, taken in my home office today rather than at work):


It's super easy to clean out the teapot, I just ran water through it a few times. The infuser basket took a little more work, but no more than 30 seconds or so of running under the water to make sure I got all the leaves out.
The teapot has a lid, to cover the tea while steeping.
The infuser basket lifts out when the tea's done steeping.
I was able to transport the pot by the handle from my kitchen to my office without any burns. It's a little warm, but not hot enough to burn you.
I'd love to see the drop that damages cast-iron!