A few things.
Re the split tip soldering gun and the Votaw key heater, I have both.
The Votaw can be bought for a bit less with a slightly uglier PSU here
http://www.micromark.com/triton-resistance-soldering-iron,7890.html
The Votaw/Triton heater is nicer to hold, takes less space (handpiece only), has springy jaws, etc. but it is flimsy and the jaws don't open very much.
The split soldering gun actually is nicer in one way. You cna open the tips wider and put them around the key cup. The Votaw/Triton can't.
I still use the Votaw often and almost never use the soldering gun, but still. BTW I also use it occasionally for soldering cables, in some situations it is more comfortable than a soldering iron (which I also use most of the time).
IMO a non-split soldering gun is just too slow.
It is possible to use a flame with pretty much any pad while the key is on the instrument and not cause any damage to the instrument or the pad. However it is pretty easy to damage some pads, especially some sysnthetic ones, with a flame. You have to do it very carefully. I still prefer the electric heater for clarinet keys once they are on the instrument because having to be less careful makes up in speed for the lost of speed that the flame gives. I still use a flame for the initially gluing the pad to the key cup because I don't have to hold the heater.
The only tricky part was that one section where 2 holes are closed by 2 pads operated by the same key, and there is some cork cushioning involved between 2 metal parts. But I got that sealing well also.
That is because of the mutually exclusive ideals of equal closing pressure and simultanous closing fo linked keys. This will only not exist if there is zero flex in the mechanism, which doesn't exist on any woodwind. The more flex there is, the more mutually exclusive these two ideals are. This is one of the main reasons why saxophones are more difficult to adjust.
The "formula" John wrote is the way to get that flex to be as little as possible. There's also noise to consider which is why you can't use even firmer materials.
Re the cork glue, I really don't like pad glue (i.e. hot glue or shellac). You need the heat source which is more hassle and it is not really faster considering everything you need to do to glue this way.
I am not sure why some people have to wait 5-10 mintues with contact glue. I rarely need to wait more than two minutes and for small key corks (as opposed to tenon or neck corks) rarely more than a minute. It's not rare that I need to wait not more than 30 seconds. I am guessing it might have something to do with others smearing it with a brush, which will never make it very thin, so it takes longer. I prefer to smear it very thin. Using hot glue will probably not really be any faster. Unless I'm only gluing one cork, by the time I smear glue on the last of the "series" the first one is ready to glue.