I take it you're not supposed to grind it off... I used 60/40 rosin core stuff, and this ancient stuff I found that is thicker but when you melt it this icky yellow stuff comes out (Acid core comes to mind)
yah to my knowledge that is an Acid core (only good for like plumbing stuff) I went to the local place and spotted a nice pen solderer 25 WAtts, it had some small tips and on the package said it was ment for fine solderin and hobby stuff didn't get it yet. think that'll work ( it was only 9$)
watch the exhaust on the gas soldering iron, it can do damage its very hot air that is exhausted out!
i got 2 diff (old) weller irons which seem to do the job well, got a load of diff sized nibs too which is quite cool, just remember to let the iron col down b4 you try and change the nib, else it hurts.