Been there, done that. I found a method that works very well. I have also used it on stuck seat posts with 100% results. First I am assuming there is some of the stick outside of the frame or just about an inch below the tube. If it is not flush then cut it flush about an inch above the tube. Drill an 3/16 hole down the center about an inch and a half deep. Put a 1/4 inch wood screw into the hole and tighten it about and inch into the stick. Turn the bike up side down in a stand. Put the back end of a claw hammer over the screw head. Take another hammer and whail at the head of the hammer that is hooked over the screw head. Keep at it and it will come out ever so slowly but surly. Don't go at it to hard as the wood can strip. Lube the stick with WD-40 after you insert the screw. You can substitute a crow bar with a claw on it, that works well also. Good luck, all else fails, cut it flush and get a brace and bit. I have one that is almost the exact size of the seat tube and it can slowly bore it out.
Ray Homiski
Elizabeth, NJ