You could, of course, create gel layers, and the determining factor in stability would be the firmness of those gels. However - and I suppose this is just a hunch - I seriously doubt that a gel firm enough to hold the weight of all the heavier layers above it (and you are asking for at least 3) would really be drinkable, unless you're aiming for the consistency of a "Jello shot".
A better idea, in my opinion, would be to simply change the densities of certain layers, and an effective (and tasty) way to do that is with sugar, or more accurately, sugar syrup. There's a type of syrup used in bartending called Gomme Syrup, which is a thick sugar syrup with Gum Arabic added to prevent crystallization (among other things).
Sugar, by itself, has very poor solubility in alcohol, but sugar syrups and gomme syrup in particular will have few problems, considering that's already how many mixed drinks are made (like Whiskey Sour). If you're feeling really adventurous, you could also use sugar alcohols such as sorbitol or xylitol, which dissolve readily in ethyl alcohol in solid form. However, these are much more potent (sweetness-wise) than sucrose and some people report gastrointestinal reactions, so use at your own risk.
Sugar syrups are very dense, so if you mix them thoroughly with a particular spirit, you'll end up with a heavier (and sweeter) version of that spirit. So to make your palindrome, start with what you'd normally put at the top (say GM for the B52), mix it with syrup (it shouldn't take an excessive amount - maybe 20-30% by volume, but you'll have to experiment), and layer that on the bottom. Then take the next-lightest, mix it with slightly less syrup, and continue. Once you reach what would normally be the densest liquid, layer the drink as normal up to the top with the "pure" spirits.
The more layers, the more math you'll have to do, because you'll need to make sure that you add just enough syrup to layer 2 so that it's lighter than layer 1 (bottom) but still heavier than layer 3, and so on. Unless you're prepared to make the drink very sweet, you'll need to be fairly precise in your calculations.
Disclaimer: I haven't yet tried this myself, as it's the first I've heard of anyone trying to do this. However, I see no reason why it wouldn't work with proper (careful) layering technique. In fact, I remember doing something very similar all the way back in primary school, called rainbow in a glass.
There are even a couple results talking about whether it's even safe to mix with alcohol.
I think this is the interesting part of this question: you obviously can use durian in a cocktail, but should you?
As you point out, there's a question of safety. There are at least two reasons to believe that mixing durian and alcohol might not be entirely safe:
One study suggests that a component of durian can interfere with alcohol metabolism.
There's evidence that eating durian can increase blood pressure.
For most healthy people, the risk associated with drinking a durian cocktail might not be all that great. On the other hand, sharing a cocktail with friends and family should be a safe, enjoyable activity that doesn't require interviews about the imbibers' medical conditions and the signing of waivers.
The last thing you want to do as a host is to offer your guests something that you don't know to be safe. There are hundreds of other fruits available for use in cocktails, so I'd steer clear of durian until more is known about its interaction with alcohol metabolism and blood pressure.
Best Answer
Yes, it's safe.
Silver tarnishes easily, particularly in contact with sulfur-containing foods, particularly egg. The tarnish is not hazardous, and can be cleaned off with silver polish or with DIY chemistry like in Tetsujin's answer. Black tarnish doesn't form readily on its own, so if you're not planning on using eggs in your cocktails then cleaning off the existing tarnish will likely last you a while (it'll be bright silver initially, but will quickly tarnish to a dull greyish silver). However, it can also be ignored (which was apparently the approach taken by the previous owner).