What the exact issue is, I'm not sure. But from looking at your pics, I noticed a few things:
Here http://i.imgur.com/d1Po9jI.jpg the ends of the wires snip them to about half the length that they are. Also snip the legs on the mosfet to about halve length. I can see flux in that picture, make sure you clean the flux off with a qtip soaked in 91% isopropyl alcohol. Be absolutely sure that the legs on your resistor are only connected to Gate and Source. DO NOT let them come into contact with the Drain leg or tab.
You're mixing both solid and stranded wire. Use stranded only. Stranded is easier to solder to. The solder will wick into it and also create a better solder joint.
Electrical tape sucks. Don't use it. Either use either heat shrink or carefully apply liquid electrical tape.
As long as all of the components and battery contacts are properly insulated, covering the entire inside of the enclosure with insulation is unneeded. If you haven't, with a pair of needle nose pliers take your battery contacts out. Snip the little solder pin on the bottom of the contacts. If a little nub remains, use a grinder to get them flat. Be 100% sure that the battery contacts DO NOT make contact with the enclosure. The positive contacts would create a short and the negative contacts making contact would cause auto firing.
Make sure your batteries are properly wrapped (they look alright from the pics). Also, make your your lid is NOT making contact with the battery contacts. If the lip of the lid is touching, file it down where needed. If the bottom of the lid is touching the batteries, make an insert that would insulate the bottom of the lid.
You mentioned buying your mosfets from three different places. Buy them only from electronics parts distributors. Mouser, digikey, arrow, sager... others you may find searching for parts on Octopart. DO NOT buy from ebay, amazon, aliexpress... they will very likely be chinese counterfeits.
