My understanding is the move system is automated. There are conflicting reports on results from submitting a support ticket. The response has generally been they have no ability to manually move anyone. The conflicting reports are from players who were moved relatively soon after submitting a ticket. No way for us to know if it was coincidence or not.
I was in the same position when I first started playing. If not for finding a great FS, I might have become one of those dead cities! I started in March and they moved me in mid-July. I read the FAQ's on the support page where they explained how it worked, so I never submitted a ticket myself as it did not sound like they would be able to do anything. By the time I was move, I think it was 6+ rings explored out from my city and when all the cities turned to gold mines right before they moved me, there were 2 cities that weren't gold mines. The idea is they delete inactive cities (by their definitions; there are some cities protected whether they are ever played again or not) and then they start moving players on the outer edges of the map toward the center. You have to fit into an open slot where the boosted goods provinces around your city are the same as where you are now. If active cities all move toward the center, you should land in a better position. It just doesn't always work out that way, because of protected cities that for our purposes are inactive/dead. If they'd find a way to move those to the outer edges if they don't want to delete them, that would help. Finding an FS that's a good fit makes this game so much easier/more fun in general (the good fit part is crucial). Finding one when you've landed in the tumbleweeds section is essential. Having players to trade with and visit/get visits from made a world of difference. Still, when they finally moved me, I think I made daily map visits for the first few weeks to everyone in my world as well as FS members, lol. That's not such a big deal anymore, but there was no mobile app then, so it was time-consuming to do that on the browser! I made sure to uncheck the 'move me' box in settings when I got placed here and I'm still pleased with my neighborhood 1 year+ later.