Those weren't DME-DME, they were VOR-DME. I don't know of anything that did DME-DME in small piston GA.
Speaking of DME-DME, how does it disambiguate between the two points that are generated by specific distances from two stations?
This is stuff I know well...
The rho-rho position solution works similar to how GPS works. Two DME stations form two intersecting spheres of radial distance information and are disambiguated by knowing the signal strength in dB and using rising values to determine a 2D Line Of Position (LOP).
By using a third DME, the additional sphere of distance provides two additional points of intersection and since only one of them can be above the Earth's surface, a 3-D position can be determined and an altitude above the datum can be calculated.
This rho-rho and also rho-rho-theta stuff is used for GPS denied navigation for "special people."
All this calculation is done in software and is included in certain DME transceiver units. Very expensive, for special purposes...