Thanks for the pics. Too bad resolution is too low to read markings. You can clearly see the separation between the grounded and floating part of the circuit. I don't see anything that looks like a heated zener reference, like the standard LM399 you expect to find, at least in 6.5 digit models. Dissipation of linear regulators depends on voltage drop over the regulator and current. Since this meter uses only linear supplies to reduce noise in the circuit, it probably draws a fair amount of power for a TO-220.
My guess is that the DM3068 uses at least a different voltage reference (maybe selected, like all the big boys do), and maybe different ADC circuit. I wouldn't count on a DS1052E-style hack. Also the community of Rigol bench meter owners is a lot smaller. Plus calibration is much more critical.