Wow I never knew about all the bts drama of this film! Also found this illuminating:

Frank Mancuso, Sr. – who had been intimately involved with Star Trek ever since Star Trek II: The Wrath of Khan – , did not really want to end the Original Crew run on The Final Frontier low note, especially with the 25th anniversary of the Star Trek franchise coming up, and wanted one more film, but found himself seriously hampered by the strictest of budget limitation: under NOconceivable circumstance was a potential new film to exceed the budget of The Final Frontier, not even by one dollar.