Agree completely wit Eric. the frame needs to maintain it's geometry so a documentation can be done (a jig set up with the frame in it) before any tube is cut out. You need to have a frank and full discussion with who ever you have repair this frame. When does he/she communicate with you and when can they just continue with the process.

Yes cut the tube (a TT) close the to lug's edge then ground out the "back wall" of the ST and HT. This allowed a full depth grinding out of the TT layer within the lugs. In theory one can look for the color change as the material is ground away and the filler layer is revealed. I wasn't able to see this and ground away more then needed. Once at this point the rest was relatively easy. the frame can be sprung apart and a replacement tube installed then brazed in. I left the tube a tad too long and ground down the slight protrusions in the ST and HT. There are more details but this is the short version. Andy