Given that the portrayal of Native American culture was hardly the episode's strong point, I don't see why it would be desirable to keep that part and ditch the rest.
The episode's portrayal of indians was neither outstandingly bad or good. There wasn't enough there to really get excited about.
I think it was great that TREK acknowledged that there
were American indians by showing them, instead of the backhanded reference in "The Omega Glory". For that reason alone, "Paradise" gets a pass.
If I could direct a remake of this ep with the original cast and sets, I would have Kirk leading a landing party that included a 23rd century-Earth indian, sent to study the native culture. (Let's call him Youngblood. He could be a Starfleet crewman or a civvie xeno-anthropologist.) When Kirk is lost in the obelisk, Youngblood offers to stay behind to look for him. When the Enterprise departs, Youngblood finds an injured Kirk emerging from the obelisk. The Amerinds find Youngblood aiding Kirk at the obelisk, and offer to care for Kirk.
The Amerinds are intensely curious about Kirk and Youngblood, what they were doing at the obelisk. They explain their tradition that the Wise Ones taught, to awaken the Blue Flame in times of the storms. Kirk takes time to heal, and has trouble remembering what he did to fall into the obelisk. Evenutally, he heals and the Chief accompanies Kirk and Youngblood to the obelisk. Kirk is able to figure out how to get inside, but they have no idea what to do next.
The Enterprise fails to deflect the asteroid, and returns to Amerind ahead of it. As the sky darkens, Spock and McCoy return to the obelisk and find Kirk leading the Amerinds into the safety of the obelisk. Youngblood is tampering with the controls, trying to get it to work. Spock presses "the right button", and the asteroid is deflected. Youngblood is able to decipher what musical notes the Amerinds should play to access the obelisk. The Amerinds celebrate and gave thanks to the visitors, who then peacefully return to the departing Enterprise.
Not quite as dramatic as Hollyweird "indians" throwing stones? Maybe not, but if it were written well I think it would've been just as entertaining if not moreso. Insofar as Kirk yearning for the Amerind "paradise", this story could illustrate it as being "so close and yet so far" without the silly amnesia subplot.
Oh, and the thought occurred to me that it would be doubly interesting if Youngblood were a woman, maybe a CPO. Think of Kirk referring to her as "Chief Miramanee Youngblood" in the presence of the Amerinds, and that they conclude that Kirk "must know the Wise Ones". (No, I was not thinking of a romance between Kirk and Youngblood; but rather a tension similar to what Kirk had with Dr. Helen Noel, but this time on a professional level without the romantic overtones. An ailing Kirk could insist on ordering Youngblood to "go to the obelisk" and not worry about him.)