I was in a similar position as you, I got my license when I was 28, although I didnt go to school for ATC, but I was working mainline Delta on the ramp. My original plan was to try and go the internal route at Delta, I had a few years in and thought that would be the best option. While still in school I applied and interviewed at Compass (they came to our class and interviewed 4 of us), more or less to see what the interview was like. Well I ended up getting a job offer, and after thinking it over and talking with others, family and friends in the business, including a sector manager at Delta, I decided to gain actual dispatch experience rather then hope I get in as an internal some day.
So I took the job at Compass, left my mainline and took a good pay cut to do it. Worked my way up at Compass, and was recently hired by United. Everyone's situation is different, but my advice would be to start working as a dispatcher now. Southwest has already said they are done hiring large classes. I don't know if that's true, but that's what I heard, meaning that its just going to be harder to get in internally or externally. I'm unaware of their internal hiring polices, but you could be among a large number of internals trying to get in. But if you really want to be a dispatcher, I would suggest getting out there and start dispatching. I honestly couldn't even imagine going to a Major without any experience, because they expect alot more from you.
As you brushing up on your skills. Yes, do that. During my time at Compass, I became a supervisor and was involved in interviewing new dispatchers, and its extremely painful interviewing people that dont study or are out of touch with there skills. Make sure you know the basics when you interview. Reading weather, deriving alt mins, reading plates, 1-2-3 rule. Know the 101 stuff, and be confident in it. Don't expect a regional to be ok with the fact you dont remember anything from school, because there are alot of candidates out there just coming out of school. As to where you can do this, I wish I could help, I'm not aware of any kind of refresher courses. Maybe take a PPL ground school class? You can find those for cheap or even free sometimes, go over your old notes, talk to current dispatchers (use this forum). Do whatever you need to, to refresh your knowledge.