Major Vibration In Neutral

My first guess would be a bad engine or transmission mount. The drive shaft should vibrate whether you're on the gas or not, but a broken mount could cause the car to shake in neutral because you've got no engine load (torsion) on it.

Does it shake while stopped neutral as well, or only while moving? What kind of shape is your balancer in? My next guess would be the rubber in the stock balancer. They tend to rot out over the years and I've seen them turn, even fly right off before. That'll throw things out of balance in a hurry, although you would normally feel it in gear as well.
 
A driveshaft/universal joint problem will not cause the car to vibrate in neutral so that's ruled out right away. The problem is more likely to be bad engine mounts or a bad harmonic balancer. Check them out.
 
My next guess would be clutch. It’s possible it has fragmented on one side. While engaged and under power, you wouldn't notice it because it is essentially one with the rest of the drivetrain. But when allowed to free wheel in neutral, you would feel it shake because of its lopsided and therefore out of balance condition.

I had a brand new stock Valeo clutch disintegrate on me a couple of years back when I still had my Fox and the symptoms were very similar. When it finally completely went south, I couldn't get the car out of gear. It could even be an alignment issue. A worn front bushing in the trans could cause vibration in the drivetrain when there’s no load on it.
Had you by any chance been doing any hard power shifting, or quick downshifting before this happened? Are there a lot of miles on your T5?

My grenaded when I dropped from a lugging 5th to 2nd to pass a car. It must have had some defective rivets. :shrugh: