Doug - I have land West of you in Hope with similar sink holes. No luck filling them in either. Its essentially a half buried hour glass with one part as an underground cone. Conversely, if you were successful in filling it, what processes has it caused to change underground? Does it divert underground streams directly to your new basement?
On our land I can actually align the sink holes across multiple neighbors land and almost plot the line where the next sinkhole could be. This covers nearly a mile of surface distance with 5-6 holes that you can eyeball (or w/aerial photos)..kind of like playing connect the dots. Perhaps you can do this to determine a direction of the underground flows???? I'd also recommend getting sonic maps before building.
Good luck