Argh. I could not sleep until I solved this. But I'm confident I have the answer. It requires both gravitational gradient and rotation to produce the correct tides. If you look at the force vectors of each individually, neither produces the correct result, but the sum of the two vectors at each point balances perfectly. When I get in to work tomorrow, I will create and upload a diagram that will make it clear. If I do it tonight, I'll be asleep on my kb tomorrow. For now, it will have to live in dry-erase on the whiteboard in the kitchen. I'm only posting now (in my scivvies) to give my brain a passing chance at sleeping.