Well anything that will increase the ash pit storage area will make the unattended burn time greater. The two options are a pit or raise the unit. Neither gets the ash outside. The ash created by my AHS is easily vacuumed. Now I'm not talking about any piss a$$ed dust buster but an industrial vacuum like a Clark or one of the units oil burner service techs use. Sucks up all the unburnt coal and breaks up the little clinker chucks. Now my clinkers are not true clinkers, just slightly fused ash, no glassy lumps. A wood shop sawdust and wood chip ducting system would be great. These have a cyclone separator that drop the debris into a trash can. Locating the cyclone separator outside would be ideal. You would need some kind of intermittent operation timer and a way to keep it from reversing the draft through the coal bed. With a large enough unit you could even vacuum coal.
How about another approach? Make something useful with the ash in your basement. When I was a kid I had my own workshop. An old outbuilding that once was a chicken house. It was built like a brick $hit house. I never could understand why, solid block that was stuccoed. Only recently did I realize it was make with home made solid cinder blocks. Someone long before me or my parents made a lot of solid cinder ash blocks. So ... take the ash your boiler makes every couple of days, mix with portland cement and water in a little electric drum mixer and make blocks. Use them for retaining walls, coal bin walls, etc. Make enough of them and you can build your own Egyptian pyramid!