They can be rewelded.....but it's usually very tricky, and often doesn't come out well. The most important step in any "feather" pattern is when you stack/weld the tiles... it pays big to take the time and effort to prep the stack of tiles with extra care, to ensure the best weld(s).
When it comes to hot cutting the stack, the level of heat in the billet, and the geometry of the cutter determines success or failure. On one hand you want the cutter to compress/pull the pattern along the "cut", but if the cutter geometry is too obtuse (as I think it was in this case) the cutter will "drag" too much, and you get the delaminations. It's common for me to create different hot cuts, depending on the billet I'm cutting for "feather". I generally will make a cutter with a convex edge, leaving the actual edge with about a 1/16" flat...then round that out and POLISH it. In my early attempts at creating feather pattern, I tried many different materials for cutters.... most ended up "welded" to the billet. I've found that cutters made from H13 steel seem to work the best for me. I've also purchased wood splitting wedges, reground the cutting edge, and had good success. Ideally, you want a cutter with not only the correct edge geometry, but also long enough to go all the way through the length of the billet, as well as being thin enough so as not to spread the cut too wide. It's a fine balance, and takes some trial and error to get right.....but once you find the right combination(s), it's a big "DUH" moment.
I've tried many things to keep the hot cuts from "sticking" during the cut..... the best thing I've found to keep cutters from sticking was MIG anti-stick spray...but
it's drawback was that I could never weld the cut back together. (I suspect the MIG anti-stick spray did it's job too well) So my advice is NOT to use that.
These days I tend to use either powdered charcoal, or a powdered charcoal slurry (powdered charcoal mixed with SAE 30 oil or water) to cool the cutter, and prevent it from sticking.
The overall process of actually making the hot cut has much to do with how well or poorly things work. Don't try to cut the entire stack at once.....this is the primary reason cutters get "stuck" in a billet, and the reason delams occur. Take your time and make sure the beginning of the cut is centered and level, then only cut a little at a time....approx. 1/2-1" before reheating the billet and cooling the cutter. In general you just have to be vigilant and careful throughout the process....from beginning to end. I'm sure there are others who have more "tricks" then I do, and hopefully they will chime in and share. Just keep at it, and you'll get it!