I think the biggest problem is going to be moving the heat around rather than trying to get more heat out of the stove, because getting more heat from the stove will probably just make the basement too hot.
How big is the living room vent?
My parent's house is approx. 2000sq ft and has the stove in the basement with a vent (approx. 12"x 36") in the ceiling directly above the stove and uses the stairway at the other end of the house as the cold air return. It works well but the rooms farthest from the vent stay cool and get uncomfortable if the doors are closed and the house is only about 2000 sq. ft.
Here is a couple threads that might help give you some ideas of how to move the heat around. You can search the forums for more info.Moving heat up stairsFloor registers with Fan
Your stove can handle up to approx. 100# of coal, and it has the thermostat draft control to control the burn rate, so all other manual draft controls should be closed once you get an established coal fire going.
I am familiar with your stove but I haven't burned anthracite in one, but there are members of this forum who have so I'm hoping they will chime in here.
The automatic draft control (barometric damper) on the stove pipe can really make a difference on the operation of your stove, but it depends on how your chimney functions. The best way to test chimney draft is to get a manometer (or some kind of draft gauge) to verify how strong the draft is as well as setting the baro damper correctly. I bought a dwyer mark II gauge on ebay for about 20$ (if I remember correctly) and it works very well for checking chimney draft and setting baro dampers.
Do a search on anything I mentioned and you will have plenty to read
Also, why did you have a liner installed in the chimney? Most chimneys don't require a liner when burning hard coal.