Logic puzzle

[douglas]

I'm curious if this community can come up with a solution to this variation on the classic "one guard lies, the other doesn't" puzzle. You have all the information in the first panel of the strip to work with to figure this out. You may use a second and third question only if your first question has proven that you get them, and you must be able to identify all three heads for every possible arrangement. I haven't bothered to work out a full solution, but I'm pretty sure it is actually solvable.