Yeah you can put your neons in a 10 if there aren't other inhabitants, you could do the neons and 1 Betta if you wanted to.
I agree, it's too much space. I did want to comment on one thing though for Time Outs. Make sure you float a container with the bully in it so they can still see each other but they can't touch. If you fully remove her from the tank then you'll have to do that all over again so floating in the tank is the best way to do a time out. I usually just use those cups but in your tank you could easily float a 1 gallon so that you don't have to do water changes daily/every other day on it. But as long as the container is mostly clear you can bascially use anything as long as they can still see each other.
The point of the time out's are so they can see but not touch, this generally diminishes the want for ripping fins from the bully. Each bully is different and each need different times in time outs. I had one girl that only took two day's and she was fine but another girl needed a full two weeks in time out for her to calm down. And don't worry about removing the alpha, as long as they see each other she will still remain alpha generally. But again, if you fully remove anyone from the tank, you'll have to reintroduce all over again