Floating ground in the apt. Building

It is possible to create a Ground Reference if you're the AC source. It's possible have a transformer between House AC your new AC going through a transformer. However you transformer now become you AC and your reference you will need a larger transformer and your wiring taken to the low side of. Of course a little electrical smarts will help.

I bought that spool from VH Audio 20 years ago and cut the ground wire by 5 inches because I always floated the ground. 
yes, all outlets are in metal boxes. 
my line is an outside line with external 1 gang outlet metal box. 
my power distribution is Furutech. 

You have a romex spool with the ground wire too short? What does this have to do with the wiring already in the wall? Unless...

Did you take that romex spool to your new apartment and then connected to a new outlet you installed and then ran the wire (exposed!?) to the breaker panel and found out the grounding conductor is too short?

If the building uses 3-prong outlets that screw into metal boxes, then the entire system is grounded since the metal conduits all connect back to the panel(s) and ultimately, the building ground.

Can ground wire be a smaller gauge?

The neutral wire should be the same size as the hot wire - but the ground wire can be smaller. Normally, the ground wire carries zero current. In the event of a short (the only reason for a ground wire), it only has to carry current long enough to trip the breaker - which isn't long enough for the wire to get very hot.

What do you have fora quality line conditioner, - surge protector ?

it has to be big enough to not be current limiting like many lower priced units.

if you don’t the Audio quest Niagra 1200 around $1k is their lowest decent quality ,

ortheir 3000 model, $3k  Puritan make a decent one around $2 k 

Sorry for the multiple posts, but is the ground in the plugs hooked to the metal conduit? Or are we talking just a hot and neutral?  Knob and tube?

I’m still trying to figure out how a three prong outlet without a grounding wire passes inspection.  I’d really start to worry about what else is wrong in that building.

And move to heck out so we don’t have to read about you dying in a fire.

Can 5" of wire in the ground make that much of an impact on sound quality? Apparently,  it can. You've done the experiment.  

I didn’t create a secondary grounding system. Just extended current ground by 5 inches to reach the circuit breaker’s grounding screw. 

Sorry, none of that makes a lot of sense.  Always follow local regulations and the National Electric Code.  Do not create a secondary grounding system that is separate from the service panel's