No secret! I just thought I wouldn't bother you with it in case the oiling works fine.
Basically there are several methods taught in books, etc.
The shrinking method. This requires a special tool that shrinks the ring. I don't really like this method because it is permanent (not actually permanent, but usually requires special tools, and not so easy to reverse). What if the clarinet gets to an area that is a lot hotter and more humid for example. I also consider this method overkill and unecessary.
There is the filler method (also described in books). This can be with paper, but I've heard of some repairers using a trash can bag, or even a t-shirt. It is ok, and the fact that this is ok pretty much proves the shrinking method is overkill. However the filler is usually not all around the ring, so it gets very tight in part of it, but actually will create gaps near that. Although I don't have any "proof" this is a problem.
Then there are all sorts of glues. Super glue is a little brittle and I don't think it is glued that good to even a little oily surfaces (which the socket might be). It is also not a great filler glue. So I don't prefer super glue. Epoxy might work, I haven't tried it. It is very strong, probably too strong to be easily removed.
The method I prefer I haven't read in any book, and was taught by another repairer (Gordon from NZ who post on SOTW and the clarinet forum). It is gluing the ring with shellac. Heat the ring, smear a thin layer of shellac all around the inside of it, and while the shellac is still soft enough to act as a filler, put the ring in place. The advantage is that it glues the ring but also acts as a filler, actually a very exact automatic filler, unlike the paper, etc. It is also very easy to remove/refill if the clarinet moves to a hotter or more humid area, or in extreme weather changes.
Another advantage of this method (to a customer) is that it is relatively fast and only requires tools that almost any repairer always have (nothing special or expensive like the shrinkning tools, etc.). This means a customer can wait a few minutes while this is done and it is also not expensive.
I guess you can use a different type of heat melting glue. Shellac is harder (when it cools) than other heat glues, so it gives more support to the ring, but another heat glue would work mostly the same with a bit more accomodation as a filler (not an issue IMO, so I prefer the extra support of shellac). For comparison, imagine leaning on a pillow, which is soft and will take the shape of your hand, and leaning on hard floor, which will not change but will support your hand much more.
Ben, I am not sure there is anything wrong with your method really. Maybe it is slower (takes longer to dry) and maybe less elastic than the sheallc (i.e. offers a bit less support).
Nitai