Wow, CNCed aluminum case! That is impressive indeed! And it does make mod things difficult if you want to leave the case untouched.
The CNCed top is untouchable and the bottom aluminum plate, which could easily be replaced for another one, drillable, does not give access to the components.
The only thing I can think of is replacing the case with another one, metal or acrylic. A way should be found to secure the front plate, and of course the back of the new case would have to be drilled for the external connectors.
OTOS, the power supply would be on the same case, as on the DX7s, with the regulators closer to the power pads on each chip, and the output RCAs would not need long wires.
I'm not sure MELF resistors are better than through hole types. They are better than SMD types, apparently.
No, copper tape shouldn't make any audible difference for shielding. IMHO, I think the metal case is to stop RFI to go out, not to get in.