Pretend he's a mascot dressed up as Abe and put the cabin near SP so he can mingle with the other entertainers. Or make a theme park addition based around him as a "historical attraction".
There are lots of ways to work him into your town believably if that worries you.
That said... if you're a completionist, you also have a space alien and talking toys wandering around your skyscraper made of popsicle sticks. Suspending reality shouldn't be that big an issue in the Sinpsons universe. ;)