I still don't understand the use of the term "mechanically balanced" in this context, it sounds like you're just talking about adjustable 2nd stages, regardless of one spring or two. Of course, it's common for the dive gear industry to toss around 'technical' terms, inaccurately, in hopes of selling a few more regulators. "Overbalanced" regs are an example of this.
Balanced valves are supposed to automatically adjust so that changes in supply pressure have no (or little) effect on the functioning of the valve. Typically this is done by routing supply air so that it exerts force on both sides of the valve, essentially canceling itself out in terms of influence on that valve. That's "pneumatic" balancing. The only "mechanically balanced" scuba valve that comes to my mind is the Sherwood style 1st stage floating orifice, where changes in supply pressure change the position of the orifice, which in turn compensates for changing downstream pressure on the HP seat. I suppose the closest thing to that in 2nd stages (that I can think of, I'm sure there are other examples) would be the floating orifice seat-saver like on atomic 2nd stages. But that's not really mechanical balancing, it's just a tricky way of keeping the orifice off the seat until the reg is pressurized.