OK, so I didn't rebuild a T3, yet, but I did rebuild two CE3s with mixed results. Some overall comments first.
Kanthal wire is a pain in the ... to work with. I bought twenty feet and it came on a small spool like sewing thread. One slip of the thumb and SPRONG! The came about a half our of slow, patient, rewinding punctuated with a lot of swearing.
All CE3 are not created equal. The first one I tried, one of the originals I think, had the coil leads glued, yes, glued into place. Getting them out was easy, cleaning those tiny holes out sure wasn't. Took lots of time with a very thin sewing needle, I can be very determined, AKA obsessive/compulsive. The second one was a breeze, not glued in at all.
I used 34 gauge for the first attempt, glued model, and used five turns for the coil which yielded a three ohm coil, a little too high. For the wick I used 2mm silica at full size, which turned out too big to get back into the cup. So, a second coil was wrapped around 2mm with two strands removed. That fit in quite neatly. Overall time for the first one was probably close to half an hour, not very productive at all, but it worked fine after letting it sit for an hour to saturate the wicks. I think the vapor output could be better an will be trying other wick setups.
The second one, I used 33 gauge and the same 2mm minus two strands for the wick. The coil came out at 2.6 ohms, a little more like it. I don't think it took more than five minutes. It worked flawlessly from the start, after a half hour soak. Again, I want to try different wick setups, maybe minus three strands.
Overall it was quite easy to do, other than the glue in that first one. With a CE3 only one lead has to point down. The shell contact is folded up against the ceramic cup and the center pin lead does exit through the center of the grommet which make it a little different from a T3. With a little practice, and no glued coil leads, I can see this getting done in just a couple of minutes resulting in an endless supply of CE3s for me.