So to clarify...u have used a voltmeter and have tested the lives for the radio!?
Do u get a constant live without ignition?? If so....then i dont see how wiring a new live from the battery will help....if you decide to try this anyway....all you need to do is assure you have a fuseholder in between somewhere to prevent any future shorting of the radio and locate the fuse holder somewhere accessible.
but if you're getting a LIVE without the key in the ignition, then that should assure that the radio holds its memory which should route in line to the yellow cable of the radio power lead! you could if you want wire both red and yellow to that LIVE cable which basically keeps the radio on even without ignition, but you just got to remember turn it off everytime or remove the face which is technically switched off without it!
Did u look further down the original VW wiring for the radio to see if it had been compromised in anyway? any scotchlocks or connectors attached anywhere that may be catering for an external source...i.e...your alarm?
wel, if you have tried everything else, then by all means try routing a new cable from battery..or even just trace a patched in lead from the fuse box battery LIVE...same thing realy! or if for a quick diagnosis...jus run a cable outside the car into the car door to the back of the radio just to test your headunit..if you find that method is effective, then u can decide to route that cable properly! keep us posted on how u get on!