I was really impressed with what we were able to get done with the compost situation. We took out many wheelbarrow loads of dirt out of the bins as we transferred the material. With an empty bin we can start fresh.
I really think that most of our compost problem stemmed from making new garden space where there was once grass. We threw so much sod in the bins and the sod was mostly soil. Soil doesn't compost.
The full bin is mostly carbon rich material - plant stalks and straw. It could really use some nitrogen. I'd like to suggest adding grass clippings to the bin and mixing them in for the next month or two. Stopping by July 1st at the latest to let it cook. That will give it July, August, September and October before it freezes. By next spring I think we could harvest a decent batch of compost. There will be chunks that will not compost because the woody items didn’t get shredded, but we can pick those out and add them to the next batch. I think we have a decent chance of heating the pile up with grass clippings and I can get a bunch from work. We could add manure, but I don't have a good source for that and the smell can be offensive if you're not careful. Someone suggested human urine, but I'm not sure the authorities would appreciate that. Although it would work very well with less work. :)
In the empty bin, I suggest we pile everything that gets added in one end of the bin. Leaving the other end free will allow us to turn the material easily. I thought about putting woody material on one end and other material on the other end, but I don't think there will be much woody material to add now that most of last years stalks are in the full bin.
I'd be willing to make some signs to post on both bins with the rules you laid out below as well as the additional instruction of piling material on one end.