MJF didn't struggle for all that long. As he said (if you haven't looked at the God Thing page), "How much work? Probably two solid weeks, spread out over a few months. I produced an outline and a sample chapter, then went into revisions on the outline." And even then MJF and his editor intended to be faithful to the intent of GR's manuscript, not to try to retrofit it so it would be compatible with TMP and beyond.
Not long after it became obvious that the MJF version wouldn't be happening - despite the cover art of the proposed Simon & Schuster audioworks appearing in the old Capital (now Diamond) Comics Distributor catalogue - I was able to ask Majel Barrett - in person - about it at a Brisbane (Australia) convention. She addressed her answer for the whole audience.
Essentially, she had been asked by Pocket Books to give the GR Estate's perspective on MJF's approach to completing TNT - and had the power of veto - and she said that MJF had proposed adding new characters and events (which, she understood, was an essential thing to do to take Gene's story to novel length) but she wasn't sure it was working. She mentioned that she had no problem with MJF's other writing, but this wasn't how GR would have expanded "The God-Thing". So she asked that the MJF version not proceed and handed GR's material to David Alexander to work on it instead, based on the Estate's satisfaction with Gene's official biography.
That was really the last we heard of it. Alexander had no deal with Pocket Books, ASAIK, so even if he ever finished working on TGT, and it met with Majel's approval, it still wasn't a given that it would be something Pocket Books was willing to publish. And, of course, Pocket had, and still has, the exclusive license on ST text-based fiction.
I reckon the best hope now is if Majel was to put out a "Collected Unfinished Works of Gene Roddenberry", and include the raw, unchanged version of TGT in that. But, I guess, the audience for such a book is much less that the sales TGT would have garnered as a "lost, last novel from the creator of ST" - in hardcover, S&S Audioworks and, a year later, a MMPB - that would have come out at the peak of Pocket's ST popularity/sales.
The horse has bolted. The opportunity has passed.