Tags are easily removed, with a little care. They grip around the edge of the tank, and have a couple of "spurs" that lock them on. If you're careful, they'll usually come right off without damage. Be careful of weakened (rusted) metal - it's pretty thin steel.
I have not had any of my radiators rebuilt as yet, but a fellow Z owner near me had his rebuilt by a shop in Nashville. Swears it's dead nuts, and knowing this owner very well, I'd take his word for it. His Z has been in his family since the early 70's, and he is very particular about it. I suppose it's too late to get the source for you, but according to him, the 3 row core, exact duplicate, is available. I intend on getting mine done at the same source he used (whenI can afford it).