Open the Damned Bottle
I can definitely sympathize with the need to keep this artifact intact. To me, it should be preserved and it should be cared for and I think that this museum has done a remarkable job.
Now, open the damned bottle.
Use fancy gadgets and whatnot, and open the thing, and extract some of what's inside, and study it. Open it inside of a vacuum, if possible, and prevent air from getting inside. No one expects it to "taste good" or anything like that. But, from the chemical components inside, I'm sure we could learn a great deal.
Just by having a look at the kinds of materials used to make this wine would shed a great deal of light on agricultural practices and things like that. The wine was probably bottled in the German wine region, or perhaps elsewhere. That would be worth knowing as well. And, there are things we just don't know that could come from studying this bottle.
The air trapped in this bottle is 1,650 years old or so--that, in and of itself, would be worth studying as well.