How Much Would It Cost to Put Braces Back on After Taking Them Off?

If the issue can only be seen when looking into the mirror from 4 inches away, then you likely are at a point where it is "as good as it gets". Quite often, when it comes to many aspects of dentistry, perfection is impossible and "close enough" is the only possible outcome.
Having said that, some retainers can be created that are active, meaning they are designed to move teeth slightly and "finish the job". The fee for this will vary by city and area as well as how much movement is needed. The best answer would come from your dentist/orthodontist.

Although we all strive for perfection, sometimes tiny details are not visible until after the braces are taken off. It is a little discouraging for us as doctors as the tools are gone. I would definitely speak with your orthodontist. It is quite common for them to be re-treated for a short time at a reduced cost in order to just cover their expenses. It is possilbe also that removable appliances such as retainers can be used with some good success.