I see that the OP lists chrome on his list of steps. Chrome is a big flag up the pole. If the frame already has chrome then that needs to be removed (chemically is far led damaging then mechanical removal) before any brazing is to be done. If the chrome is to be added after the modifications are done then care must be taken with the brazing to have no pocks or gaps (ask any English made Raleigh retailer about this) and to have thorough cleaning after plating to remove the corrosive cleaning agents.

Doing this kind of work on a frame can be much like a cancer. The resulting condition of the frame has less ability to handle further insults (like chrome) to the metal.

As to the actual headtube removal- No need to use any heat. Just cut down the down and top tubes a tad less then the intended shortening needs. File off any remaining lug tips, miter and reassemble with new lugs and head tube. Oh and don't forget to bend the down tube to keep the head tube's new bottom the same height off the ground. Keeping the head and seat tubes in plane will be the least of the problems...

I do like Dancingbear's suggestion to just do it. The Op might end up with egg on his face and learn why we don't encourage this type of job. Andy.