Ok Andria, I've kicked around commenting on this thread for about an hour and I just have to comment. What I'm saying might be said later on, but I had to comment since I went through some of this myself.
Pardon the chopping of your post but I wanted to focus on just a few points.
Ok, so a higher number gauge means a finer wire? Because, as I was doing the dry-burning, of course I really looked at the coil, and that is some very fine wire...
...I have one coil, as I said, that I think is just toast; I checked the two misbehaving ones again just now, and one of them is almost certainly just gone; it's now registering 3.2 ohms...
...I think my idea of switching over to cartomizers rather than using tanks all the time is a really good idea...
... the promise of "rebuilding" to someone who may not be capable of that level of mechanical ability, if I can't even figure out how to make them stop leaking. Really it all just makes me want to cry, like I'm just throwing good money after bad, building up my hopes over something that refuses over and over to work right...
Andria
First off, yes, a higher number (meaning higher gauge) wire is thinner and that also means that it has a higher resistance per inch. In terms of clearomizers, like your T3S for example, tend to use very small wire like 32ga and sometimes up to 36ga wire because they have a very small space to put the coil/coils into. The use of that smaller (higher resistance) wire means that they can make a coil with the same resistance in a smaller size. Here's a pic that might help explain wire size as it relates to resistance:
Secondly, your coil that "gained" resistance as is was used is simply the wire burning up due to being heated as its used. When it gets hot the wire in the coil actually gets smaller in diameter over time and therefore the resistance of the wire goes up. To a small extent you can increase your power/voltage/wattage to compensate for the change but it will only work for a little while.
Now finally about the last 2 comments, there is little I can say about cartos as I haven't used them, but there are many that do and enjoy them a great deal. As far as tanks leaking, almost every tank I have every had has leaked... always.
Rebuilding does have a bit of a learning curve but I would make a suggestion that may be quite a bit cheaper and more useful for you. If you already have the wire and something approximately the size of a precision or eyeglass screwdriver, I would suggest that you consider a RDA or dripping atomizer.
A couple reasons I say that; the coil you would build for something like that is actually less complicated than for a clearo like you are doing now. The base price (not counting shipping) is about the same as a single clearo as a mini RDA (about $9) and can be rebuilt several hundred times.
The coil in your clearo is "technically" a "nano" coil, meaning its small as h*%#! And also that its difficult to work with. The one in the dripper could be as large as almost 2mm in diameter and take only about 5 wraps to be at your 2.2 ohms. Also, if making a micro-style coil, your coil doesn't get removed when its gunked up you just pull out the old cotton wick/dry burn and rewick then you're good to go again!
My coils at .6 ohms are doing amazingly well and are over a month old already.
If you'd like more info, just give me a yell and good luck getting it sorted out!