For which we stand

Arnold Zwicky has an interesting rant about the THAT rule over on Languagelog. I know he's been talking about this on ADS-L and Languagelog for awhile now. I have to say that I haven't been paying close attention. So I'm sure he's discussed this, but I wanted to bring up my favorite prescriptive conundrum.
The THAT rule says that that should only be used for restrictive relatives and which should only be used for nonresctrictive relatives. The fun part comes when you combine a restrictive relative (obligatory that) with a stranded preposition. Inorder to not strand the preposition, you need to use the which relative. But it's restrrictive!
1. *My neighbor owns the dog that Bill gave the bone to.
2. *My neighbor owns the dog to which Bill gave the bone.
Both sentences are ruled out. What's a poor boy to do. I guess this is where you fall back on the old prescriptivist standby: rewrite to avoid the problem.