Ok, so definitely brakes then. It's got to be something somewhere. I doubt a little bit of caliper movement like you described is the issue. I guess it could be, but let's rule everything else out first.
- Did you replace the metal anti-rattle clips? Are they in the correct configuration? There's a different one for the top vs. the bottom on both the front and back.
- Did the pads fit securely in the anti-rattle clips? In other words, is there any loose horizontal play in them (besides being able to move backwards without the caliper attached)?
- Do the pads have their backing plates attached properly?