12W Antex Iron taking 15+ seconds to melt my lead-free solder, do I need a new Iron?
Your tip is dead since you have now sanded off the special coating.  It will of course still get hot, but will oxidize rapidly so that solder won't wick onto it.  This will make it very difficult to solder with.

You say the tip is supposed to be 370C (700F), but is that temperature controlled or just some open loop guess?  12W sounds very low for a temperature controlled soldering station, and also not enough to heat much beyond a little solder and a wire or two at the same time.  For example, my Weller WES51 temperature controller soldering station has a 50W iron.  Of course most of the time it's not run at 50W, but that's what the control algorithm can cause it to put out when it senses low tip temperature.

Since you just destroyed your tip (and the iron if it has a fixed tip), maybe it's time to get a real one that has temperature control.