Hmm.. Not sure whether Shoegaze can be dominant in the USA - the best opportunity would be if it replaces Riot Grrrl as the rock music of choice for female indie bands in the USA. (Difficult, because Showgaze is generally too vague lyrically to be political)
I could more easily see other bands/scenes adopting shoegaze as their music of choice than riot grrrl. It just doesn't lend itself well to strong political themes and nothing about it particularly says "Smash the patriarchy!".
I think the idea that it could be salvaged by the Internet somehow is more doable, but your scenario may not happen in the early 90s. I mean, In The Aeroplane Over The Sea and OK Computer were released in the late 90s, and Oracular Spectacular in 2007/2008.
Taking this into account, I can think of two ways that make it more popular thanks to the Internet:
- A band releases a shoegaze album in the late 90s that becomes quite popular among the "hip" kids for some reason. Maybe you could add some kind of innovation, or particularly interesting lyrics. Those who are teenagers in the late 90s are in their 20s in the period between 2000-2010, when more and more young people start being able to access the Internet and as it becomes a better promotion tool for musicians. As they blog, review music, and start their own bands, slightly younger people also start getting into it as well. That record becomes a cult record of sorts due to how incredibly clever it sounds, or something. Then you have people who were in their 20s in the 00s and people who are in their 20s now starting indie bands inspired by the sound.
- A band releases an album between 2008-2011 that appeals to the "hipster stoner" types. They also manage to have a relatively strong Internet presence, and the explosion of tumblr and its popularity among their target demographics leads them to get even more exposure. As does being featured in a TV show that said demographic watches and which has a reputation for always being ready to feature cool, relatively unknown music. Many people I know became aware of MGMT through Skins. And it was also featured on Gossip Girl.
It could also go the riot grrrl route if you still give it a stronger presence in the early 90s; it becomes more obscure following that, but a specific demographic manages to make it more popular again.