I'm just curious, would I be allowed to submit a run of a version of Cave Story identical to the original release, but only with modified/changed .org files?

Don't take my word for it, but I would assume it would have to be proven beyond doubt that the changes affected the timing in no way whatsoever, possibly to the extent of providing audio cues the original files didn't have.

But in the original music, you could make audio queues just as well.

Yes, but you can't change the audio to make different audio queues with the original music.