I can't really describe it -- it was such a bear to make *any* progress
excavating it by hand, that I never was able to make enough headway to be
certain about what i was looking at. What I really need is something like
an really durable Archemedes Screw insert off-color joke of your choice
here to get the coal and dirt and rocks out of the hole. A small backhoe
won't do it. Nothing I can seem to rent is small enough and stable enough
to get into that corner and dig that coal out.

It's funny you asked for a screw because there is something like that
called an auger and it is indeed shaped like a screw. They are used
to drill holes of any diameter in soil for fence posts and pole
buildings. The large ones can be mounted to a machine (Bobcat). One
and two person models are also available. Ice fishermen use the small
ones to drill through the ice. All can be rented. Better to have a
backhoe.

It may be possible for you to auger a hole as close as you can get or
maybe several holes. Although you would have to finish the dig by
hand it it would at least get the work started anyway. Four to six
feet is the maximum depth for the augers I have seen. Better to have
a backhoe.

If you have to excavate the coal chute anyway then it should be
possible for the sump line to exit the house in the same ditch. The
excavation for the sump line can far exceed the size of the sump it
can be a big deal.

If you can extend the ditch to where the sump line can exit the soil
then problem solved. Best practice would have the ditch go dowhill
from where it exits the house but depending on your situation you
might be able to cheat on this.