photo of install & video of movement against spring etc. would help diagnose immensely. They should NOT move vertically at all against caliper retainer spring plate once correct pads are installed correctly... only on a horizontal plane in and out against rotor. Even if you release pedal you shouldn't be able to hear any substantive pad movement.
Also, did you:
- re-check all wheel bolt torques? (97 #-ft on 987 IIRC)
- remove any caliper while installing? (if just pads no need on '04 986) check caliper bolts?
- replace rotors (sounds like no)?
- replace any hardware - caliper bolts, retaining spring, retaining pin, etc.?
- apply disc brake quiet (like CRC) to backing plates helping pads stick to caliper pistons?
- use caliper grease as necessary?
- check caliper pistons for leaks and free movement - inner & outer?
- bleed/flush brake fluid system once complete?
- keep an old pad set from each axle around to measure backs against new?
Happy to help - need some more input please.
Good luck
