Isolated Ground causes ground hum.

OK, so yes, you just created your own ground loop. :)

What you can do: 

Add more ground rods.
Bond them to house ground rod farmRun 1 ground wire directly to the ground rods, and use that for your outlets.

Then run phono grounds like normal, from device to device.

@ erik_squires

Add more ground rods.
Bond them to house ground rod farm. Run 1 ground wire directly to the ground rods, and use that for your outlets.

Not sure what you are recommending to the OP. Would you please expand.
NEC requires the equipment grounding conductor to be installed in the same raceway or part of the same cable assembly, (Example Romex).
NEC does allow an Auxiliary Grounding Electrode. NEC 250.54...  I wouldn’t recommend it. It supplies a path for lightning to enter the OPs home.

2008 NEC—250.54

Auxiliary Grounding Electrodes.

One or more grounding electrodes shall be permitted to be connected to the equipment grounding conductors specified in 250.118 and shall not be required to comply with the electrode bonding requirements of 250.50 or 250.53(C) or the resistance requirements of 250.56, but the earth shall not be used as an effective ground-fault current path as specified in 250.4(A)(5) and 250.4(B)(4).

https://www.ecmag.com/section/codes-standards/significant-changes-nec-2008-0
The Aux grounding Electrode Shall connect to the branch circuit equipment grounding conductor. Lightning loves an Aux grounding electrode.

.

https://www.youtube.com/watch?v=WlnFNTay-9Q
Jim

I would think long and hard about adding the ground rods.  If you did get hit by lightning or gave an electrical fire, it’s a sure bet your homeowners insurance may be quite reluctant to cover the loss.  To be sure, I would have a local certified and licensed electrician check out your wiring set up. 

@JEA48

As far as I know, the NEC does not specificity a maximum number of ground rods, so long as they are all bonded together. That's what I am referring to.

Best,
E

@ erik_squires

Thank you for the clarification.

Yes you are correct there is no limit to the number of earth ground rods as long as they are all tied together. They then become one electrode. One ground wire is extended and then connected to the service entrance neutral conductor in the main electrical service equipment/panel.
Jim