Do studios like MAPPA do small animation projects for the right amount of money? It seems that MAPPA only does animation they're paid to do by TV stations, so I am wondering if they would be willing to accept work from a single individual as long as they get paid.
In paper yes (http://mappa.co.jp/mappa_e/contact.html). But, it's more better if you have connection with someone over there or a representative that as one.
You might be actually also be better off contacting an animator directly though if the animation project is like really small. Since most animators are contractors / freelancers.