[Grant Bowker]

Some of the old/original tires are almost woodlike in texture....
Yes, I've honestly done it. Obviously, ensure the tire is fully deflated first. Then with some care (as for every use of chainsaw) with the saw bar at about 45 degree angle from the tire and rim lying on the ground gently work your way around the tire cutting just deeply enough to cut the carcass, no need to go through the tube unless you want to. I believe it is easier and safer to do a shallow cut for control and a second pass if needed rather than plunging deeply and risking binding. (It has never happened and I don't want to give it a chance to happen.) Leave enough clearance to the rim for your comfort, no need to ruin chains trying to cut the rim. Flip over and repeat to free the other side. Bob Carriere may have photos of the process under way. It's easier to separate the rim halves before cutting the bead of the tire off the rim but it can be done with the rim assembled (except for runflats where the bead lock gets in the way). I tend to use an angle grinder and cut-off wheel to cut the steel bead wires, Rob Clarke prefers to use a cold chisel - personal preference, they both work.
I haven't seen any tires with steel plies on CMP rims but I suppose it is possible and the chainsaw method is not suitable for these tires, check with care before starting work. I've found the process to work beautifully on the original multiple cotton/rayon/whatever ply tires (i.e. 10 ply rather than 10 ply rated), not sure if it is because of the plies or the aging of the rubber, but also used it on newer (ply rated) tires without issue.
I leave it to you to decide if I'm a fool who should have killed myself through bad technique or if this technique suits you.