I am a little doubtful as to any potential advantage in wiring the mains socket to earth. I assume there is an RCD between this mains plug and the equipment so that it can detect a fault condition and trip. And only then if pressing the RCD test button resulted in it tripping – in case the earth rod had too high resistance to take 30mA of current. I appreciate there are advantages to earthing the mains directly to a pure ground however this should not be necessary with the groundmaster installed. There is a consideration also, that many in the Hi Fi community regard RCDs as a necessary evil because they degrade sound quality, so putting in an extra one is generally avoided however this may not be terribly relevant.
Unless Mike of Puritan thinks otherwise (as my experience is not as great) I would suggest removing this secondary earth wire to the grounding rod in the garden and just sticking with the one earth to the garden from the Puritan Groundmaster.
The principle of star earthing which the Routemaster addresses is that all signal earths can equalise at a single point (the Route Master) and then go to a signal ground created by the Groundmaster. The Ground master should not be wired through an RCD as its safe on its own because it filters out the dangerous mains frequencies and only allows excess noise to escape from the system. I am not sure what is the case in your system and there are a number of details like this which I am not aware of. A photo of a sketch showing your complete wiring configuration may help a lot, including cable lengths and mains supply socket positions showing what is connected to which sockets and where.
If the hum is much worse on one channel and you are using an RCA phono plug from the groundmaster into a piece of equipment on say the left channel then it may be worth trying the groundmaster on the right channel and then both channels at the same time. This is unlikely to solve the problem but if your amp has a peculiar design it may do so.
If it’s not too much trouble try disconnecting the rest of the system and reduce it to the minimum. Amp and speakers with no input. Turn up the volume carefully – hum? yes or no? or note at which level it becomes audible. Turn down. Connect the D3 with nothing connected to its inputs and repeat. Where does the hum start to become audible? If at all, try the same with other RCA cables (cheaper cables are often better than esorteric cables at hum resistance just because they are truer to the physics). Then, connect the deck and repeat and test. I think the only way to be sure is to start from scratch and be as methodical as possible but always being cautious to turn things down in between tests and watch out for feedback when slowly turning up.