Matt,
Well done on getting this far- mine had similar problems, it would run for a limited time then soot up. Changing my meths to industrial meths helped, ideally, I need a wider wick- think mine is 4mm rather than 7mm dia that Jan specifies.
I have to contradict some of the others on the lubricant thing - I found (idea came when I started building 'poppin' and liasing with another member who had) that mine will only keep running with car engine oil (believe it or not!) Quite a thin grade but when hot, engine oil is very thin and very slippery - it also can deal with the temperature and stops unburnt products from the meths (brown substance you were talking about) from gumming things up.
Maybe the reason I need oil is that my fit between piston, valve and bore isn't as good so it needs the oil to help seal, I think the other advantage is keeping the bore clean - I don't have to strip mine down to clean, just make sure there's enough oil on and let it heat up for 10 or 15 mins before running. The longest run I managed was about 15 mins until the burner ran out. What I really need though is an oil cup at each end for piston and valve, like poppin does for the piston.
I know my comments may seem contraversial - not really, just different and what happened in my experience, worth a try though nothing to lose.
Good luck
Nick