You can probably mound the coal higher than the firebrick, the hot part of the fire is not at the top, so there would be no harm from some fresh coal resting on the top of the firebrick against the cast iron.
I too think that you should be able to cool it down some and extend the burn if you can seal it up better.. use a smoke source, a cigar, cigarette, incense stick or even a candle flame and check around the doors and vents for air leaks..
The sliding type of air vent often isn't very tight against the door, if it has a tensioning bolt or spring, tighten it up to reduce the gap/clearance.. you may even want to remove the slider and sand/ polish the sliding surfaces to make them mate closer..
A 4-500* stove temp and 250* stack is still pretty hot, I think a stack temp of 150* is do-able if you can shut down the air some more.. if you have a really strong draft this may not be possible..
if you have a strong draft, I'd recommend a Barometric damper to control the draft,, this will pay for itself in lower coal use, and longer burn times..