Here's a pic of the APE kit
Ignore the cam cover, the tube replacement kit is above. Essentially you have 2 tubes the same diameter as stock frame rails, and 4 slider bits which are a real tight fit to the replacement tube.
You cut your tubes out just a tad longer than the replacement tubes. The closer to exact the better. But you need to cut far enough forward to get the head off. That's about 2-3 in back from the front downtube. Then slide a slider onto each end of the replacement tube, set the tube into the space you have opened up in your frame rail now, slide the sliders out to cover the stubs of your original frame tubes.
The slider will be half on the old tube, half on the replacement tube. The sliders came with holes in them. Drill the stubs and the replacement tube and bolt the sliders into place. You're done.
There is no provision for replacing the triangle portion of the original frame which is also removed by you when cutting the tubes.
A machinist would be able to recreate this setup quickly I'd think.