How to make 95%+ efficiency voltage regulator?
That eBay thing is a switching regulator, aka a "switcher", aka SMPS (Switch-Mode Power Supply). These things can indeed reach efficiencies of 95 %, exceptionally 96 %. Lot of it depends on input and output voltage, and the highest efficiency is with parts that are designed for a specific input and output voltage. So the eBay thing won't always be as efficient, especially not at low output voltage or high input/output voltage ratio.  

You can make them yourself; as you can see they only require a few parts, but designing a high efficiency switcher requires some experience to choose the right parts and make the right PCB layout. So I would suggest you buy one. I guess a component cost for the eBay module will be around 6 or 7 dollar, so 2 dollar would really be a bargain.

edit
You can't use the series resistor to regulate to 11 V. At 2 A and 12.8 V in you would need a 0.9 &Omega; resistor, but when the current drops to 1 A that resistor's voltage drop will be reduced to 0.9 V, and the output will rise to 11.9 V.