that soldering iron tip is pretty cool (but its for repairing dead LCD lines due to shoddy ribbon cable connections going to the LCD (the glass), not quite this sort of thing). although i don't see why you couldn't adapt it for this, you might find it less frustrating if you do each point one by one, with a basic conical tip. not sure how the teflon coating will affect the ability to solder either. i'd guess it would prevent the solder from interacting with the iron's tip in some way, but really have no clue about this. its coated to keep it from bonding to the rubber/silicone part i'm assuming.
was just poking about and ran across this guy: http://www.ebay.com/itm/30W-Soldering-I
mp;vxp=mtr
its 10% off for the next some hours, and free first class shipping in USA. the other tip you posted seems to be aussie shipping only (at least, no usa shipping). which is fine just noticing. and i think this whole kit is cheaper than the equivalent iron alone from radio shack. the same seller has the tip + silicone kits, without the soldering iron, in their shop too for those of you with an iron that will take the tip. not entirely sure that's actually a silicone part, i think they call it just rubber in the text, but for it to withstand the amount of heat that's penetrating it just a hunch its a silicone part.
seems this is the handheld/home equivalent of the machines which make these sorts of connections in a factory. its basically the same thing, functionally at least. i like how this version can slide along the slilicone strip so you (presumably) don't have to move it each length/step of the way.
but, anyways, i picked up one of these tips with the silicone pressure/heat things and am very anxious to try it now. i've been using a large chisel style solder tip for this sort of repair (dead LCD lines), because the larger surface area, so am thinking this is going to be an epiphany of sorts. thank you soooo much for posting your find, it might even fix the dreaded horizontal lines! new tools are so much fun