If you feel the coil burns its leads, and you have no space, you can use silver wire about 1 mm diameter. Silver is not expensive, everyone can buy needed wire on e-bay or just to ask a nearest jeweler to make it. And silver is the best heatsink, so you get rid of burning issues. I made a few genesises with aluminium contacts, but now I use silver only. Very easy to make and no problem with contact and burning taste.
No need to bend the wire, just reel your kanthal.
No need to bend the wire, just reel your kanthal.