One thing to point out here: I think it is pretty hard to avoid the ST fan film boom, given that around the turn of the century, there was now a lot of people around the world with an interest in the franchise, suffering from withdrawal effect when new shows were not on the horizon (or perhaps that was just the post-TNG blues), and perhaps most importantly, having the technical capabilities and hardware easily available for making such films. Really I think that for avoiding a number of fan films being made circa 2000-2010 we would have to butterfly Star Trek fan culture and mid-to-late 90s advances in computers and digital cameras.
The Finnish Star Wreck series of ST fan films is a case in point - a guy started making simple Star Trek animations of his PC in 1992, and several increasingly tolerable installations later, in 2006 he, with a group of friends, released Star Wreck: In the Pirkinning, a full-length ST/Babylon 5-crossover fan film, with mostly poor acting and a somewhat meh script, but really top notch space battle scenes outdoing ST:TNG and B5 original graphics, painstakingly rendered on a few home computers.
What I am saying here is that these kind of fan films were made because people were short on ST-related things to watch, and now for the first time the fans could make them on the cheap and with (relatively) cool graphics. Motive, opportunity and the means conspired to make the "boom" - in different countries, not just the US.
So to avoid it - 1) remove the motive: have one or several passable-to-good Star Trek series follow DS9 and Voyager, along with Enterprise, extended for several seasons, and better yet have some of them premier in, say 95-97 to coincide with the other series for effectively taking up all the fans' time, or 2) remove the opportunity: somehow conspire to make ST fans more rare and isolated, without potential collaborators for putting together fan productions, perhaps weakening the whole fan movement around the franchise already before, or 3) remove the means: somehow make it so that the required computer hardware and software as well as relatively cheap/easy-to-use digital cameras are slower in appearing and don't lend themselves to such fan projects.
Otherwise, I am at a loss. It seems to me that it was almost inevitable that at least some fairly elaborate fan films/series would pop up roughly during the time of the "boom". The intensity of the "boom" can be tweaked with minor PODs, of course. In the Pirkinning, for example, could be torpedoed with fairly small changes. But beyond that, I don't know.