It initially sounded like what you were looking for was just a large teapot with an infuser and some sort of warmer/cozy.
The volume you are using is large, so in order to keep the tea warm it would take some trickery, but you might drink it fast enough anyway, just make sure you warm up the pot first.
The other option you are looking at is one I prefer. The electric kettle/warmer you posted is very similar to a zojirushi, which is the more widely known brand for that appliance. It doesn't reboil every time you need it, just every time you turn it on. When you turn it on it first boils the water, then it cools it to the temperature you set it for (140F for you it sounds like), then it stays at that temperature the rest of the day. So if you could keep it near you it would be perfect because you could brew on a cup-by-cup basis and always have hot water when you need it.
I'm sure a few others will add to what I've said. Good luck!
Also: The filter at the spout of your current kettle is not to filter tea. More than likely it is there in case you have any mineral buildup from boiling water so that if it flakes off it doesn't get into the tea you're brewing.
