Clive Wooley, Big Game Shooting circa 1894 states that ones heavy African battery should consist of:
A single 4 bore
A double 8 bore
A double 500 express
And a paradox
So you are on your way and headed in the right direction, too bad were about 115 years too late!

A smooth bore will do. There is a single 8 built on a 4 bore frame for sale, but somewhat above your stated budget