I found that a Harbor Freight bi-metal reciprocating saw blade can cut through two tires before losing enough teeth to become ineffective
I remember having melted rubber gum up the blade too, but I found that improving my cutting technique helped with that!
Looking at the way you cut the tire, you might've been able to save some effort by avoiding cutting through the bead - there is a lot of steel in there as you described. What I did is start my blade horizontal to the sidewall then plunge it in and completely cut around the bead. Once that was done I worked the bead still attached to the rim by hand, loosening it with a pry bar if I had to.
I just added a pic of my work. Note the intact bead on the rim.
View attachment 883168
Out of curiosity, how thick are the side walls on the tires you're taking off?