I doubt it would be as short as all that. Look at The Motion Picture Director's Edition. Not all that different in running time from the original. Just some scenes are made shorter, some moved around and other previously unfinished scenes, expanded upon and completed with new FX.
I'd love to see a more extensive battle sequence between the Enterprise and the Bird of Prey, while half a dozen fire-breathing, molten Rockmen break from under the ground to chase Kirk, Spock and McCoy back to the Galileo - and then attack the hull - before two of the triad are beamed up, leaving Kirk with no recourse but to climb away to escape them.
The problem is the film built to a climax, dependant on special effects they had no money left to give satisfactory scale to.