"Heat up that area..."
+1
Heating the area helps a LOT.
You might try a piece of hard wood tapered with flats cut on it first. You never know, maybe the wood will snag the threads and turn them out with no risk of damage. I have also used a brass rod sharpened and fluted like a broach. A steel file, broach, or tap is my last resort.
Something else you could try is cut a tap short enough to start from inside the case and maybe cut the old tube out. The tap will start straight in the clean threads. It will kill a $$ tap but is a 'not too much risk' method. I bought some 3.0mm x .35mm taps made in Bosnia that only cost $5 each...maybe you can find some cheapo taps somewhere. I ordered mine from a nut/bolt/tool outfit years ago.
BTW here are the taps for $5.40 each:
http://www.victornet.com/tools/Metric-Taps/139.html