A balanced version of this would be very, very big so that is the first major issue. There are also a lot of parts needed and to match all of them. Not under 2K$ with free labor would be my guess built to our standards.
For a balanced amp the Dynalo Mk2 would be a better fit as it is cheaper to build, it's super symmetry so you can use either a SE or balanced source for balanced output and it's performance should be on par or even superior to the KSA-5.