Rename file only if EXIT timestamps exist in it?

I realize this might be a multi-step process.

When syncing pictures from various devices some do or don't have EXIF data in them. I've noticed some from Android phones are created with a FILENAME based on the START time of a recording. Which conflicts if they're mixed in with anything that did transfers based on the EXIF recording timestamp inside the file.

I'm thinking it's going to be less trouble to handle the image and video files separately.

Is there an example on how I might best approach this?

I'm thinking:
find mpg or jpg files that contain EXIF timestamps
mangle that timestamp to see if the filename already matches
(doing math to calculate back to the start time seems like it'd be problematic)
if the filename does not match the timestamp then rename it accordingly

Am I on the right track here?

Is it possible to use AR to 'correct' the filesystem timestamps on files? As in, moving/copying has somehow changed the timestamps from their original and I'd like to 'set them back'.