SilverWook said:

It's possible they had the bare bones of a time travel story, and just lacked a good reason for them to go back to 1986. Or at least a reason not done before on the series.

There also might have been budgetary reasons to do a movie mostly set in the present.

I wonder if a Gary Seven cameo was ever thought about?

It's been so long, that I don't know if talk of Kirk and company becoming an intergalactic version of The A Team, was a real thing, or just a joke that was going around. Ditto the Eddie Murphy rumor.

The Eddie Murphy rumor was real. He's a huge fan in real life. Koenig and Takei mentioned it during one of the commercial bumpers when Sci-Fi channel aired the movies back in the 90's. Eddie Murphy made The Golden Child instead and then wished he hadn't after it flopped. The role he would've played, a UFO nut who spots the Bird-of-Prey, became the whale biologist character in the finished draft of the script.

Never heard this A Team rumor before, but that sounds awesome!

Basically, what I'm wondering is if there were other story ideas considered aside from time travel, if that was always the basic plan or if the success of Back to the Future only a year later had anything to do with it.

I looked up Voyage Home on the Trek wiki and the only interesting thing I could find to this effect was that the comic books immediately following Search for Spock had the crew leave Vulcan in the Bird-of-Prey, only to be caught by the Excelsior. When the writers heard that the next film would find our heroes still on Vulcan, they had Spock come down with a virus so the crew could commandeer the bird-of-prey from the Excelsior's (apparently quite large) hangar bay and fly back to Vulcan for the cure. Thus the comics and movies could stay within the same continuity.