I don't think Parallax mapping should be allowed - using photoshop for editing the tiles or rearranging them in fascinating ways defeats the point of an RTP & engine only jam
Parallax mapping can be done without GIMP and Photoshop. I remember being able to do it six years ago, with just RTP, and without editing. I will try to see, if it can be done.
I just looked at the Parallax Background feature of MV. If used, you may use the predetermined 15 Parallax Background maps. This is available in the map editor, and Page 3 of the Event Commands. I have not looked at my other RPG Maker engines.