Hello Rich, welcome to the forum. Burning Bituminous coal can be very frustrating because of the wide variations of the quality and burning characteristics.
That lump of [coke] that is remaining you describe as 'lava rock' is it light and porous, and crumbles in your hands?? If so, it is just the remaining ash from a shallow bituminous coal fire.
Does a wood fire burn OK in the stove? Does it create enough heat to heat that one floor of your house? I think that furnace is pretty small for the square footage you are trying to heat. This depends on the insulation and windows in the house.
Since you are not that far away from Anthracite coal sources I'd try getting several bags of Nut size anthracite coal. Build a hot wood fire, let it burn down to a hot level bed of coals, Add about 1-2" of anthracite coal over the entire bed of coals. Close the loadiing door, and open the air control on the ashpan door. Let the 2" of anthracite to get nice and hot. You can then add progressive layers of anthracite up to the top of the firebrick of the firebox, even mound it up in the middle. You want a coal bed at least 6-8" deep, the deeper the better. I burn a 16-18" deep coal fire in my boiler.
You will control the heat by the ashpan air control. The air control in the loading door should stay closed.
I believe you will find that you can maintain an effective fire for 8-12 hours with anthracite. If you can load more anthracite on a still hot fire, let it get burning then shake the ash off the grates into the ashpan, Then topp up the coal in the firebox. This way you should be able to maintain an anthracite coal fire for weeks at at time. Anthracite burns down to a fine ash, either powder or fine crumbly pieces, they don't stick together.
If you follow the above proceedure with Bituminous, you will probably have much more ash, and some fused, melted-together ash remaining on the grates when the fire goes out. This melted, fused ash is as Chris said above called Clinker. It can fuse together in sheets that block the airflow through the grates and starve the fire for oxygen. With Bituminous coal I have to clean my firebox every few weeks
Rich: check your PM's... Greg