Hire a squad of 50 to 100 Dachshunds at once! They will rush down there happily, roll around in the shit, and then carry much of it off clinging to their coats. Do this for 3 or 4 days and your shit problems will be solved! (sort of) Well, they'll be lessened anyway....

Dachshunds can be bribed with food. Keep this in mind and you will be able to attract much willing canine help in no time flat. Consider advertising in Canine Weekly, and place handbills near fire hydrants.

Oh...if the basement stairs are too steep, you may need to provide a ramp or install a doggie elevator.

That about does it. Good luck.