Without a way to get the coil glowing good it's going to be really hard, if not impossible to work the shorts out. If you can't get a device that can fire the current coil properly, you could go up to a thinner wire. This will heat quicker and hotter at the same resistance, allowing you to get a good enough coil glow going to work the shorts out. I'd really suggest 32g or possibly even higher if that doesn't work.
You could also switch your build style and try to get a perfect build right off the bat, instead of getting wire on there and then working out the issues later (the sometimes annoying glow, poke, and prod method) The easier way is to wrap your wire around a drillbit, nail, pin, anything of the right diameter.
Make sure the
coils are all super tight, then you mount the coil onto your device with the nail/pin still inside the coil. Do your adjustments and screw the wire down, so that the coil is perfectly straight up and down. Make sure all the coils are still tight and uniform.
Then remove the pin, and slide your mesh wick inside the coil. As you know mesh loosens one way, and gets tighter another way. So when sliding the wick in, roll it as needed to adjust the tightness between the wick and coil. The wick should be tight enough that all the coils touch it, and provides just the slightest bit of resistance when trying to pull it out.
This method might not always get you a 100% perfect build straight away, but it's far more likely to compared with other methods.
Also when securing your bottom wire to the deck, make sure it connects to the post at the closest possible distance from the coil. You don't want a big loop of wire going halfway around the screw before it actually gets secured, it should make a pretty much straight line from the coil, to the post/screw.