Dear RichD:
You clearly have difficulty separating the specifics of the analogy from the concepts underlying its intent.
Is there a linear combination of the 2D surface axes (representing 3D space) that can generate the "radius"? No.
Is there a 1:1 correspondence between the balloon radius at any instant and the size of the "balloon Universe" at any given instant? Yes.
See, you do understand. And if you don't agree with this, you can start with the raisin bread analogy...
David A. Smith