Wow, lots to respond to here. I appreciate the input.
The tweeters appear to be unharmed. The smoke was definitely only coming from the Woofer area (I took a brief video before pulling it outside). The house smelled like a bonfire for several days.
I know I'm likely using the wrong setup. So please don't roast me too badly LOL. I have a Carver CT-Seven Preamp and a Carver A-500x Power Amplifer powering them. I know it's probably too much power for them. Both components seem to be operating properly, so I believe I simply had it up too loudly. I'm still currently using the same setup with just one speaker hooked up.
I'll try this weekend to do what Moray James and Ricktate have suggested. If there are issues with the Amp, I'd hate to cause more damaged the La Scalas.
Regarding age, I believe they were purchased in the late 1970's by a family member. Serial numbers are 21T153 and 21T089 (blown up one).
I'm really considering just going with the same K33's. I didn't realize that was what they had come with originally. I still have not opened them up, but again hopefully I can get to it this weekend.
I'd upload that video I was referring to, but I don't see that as an option.
Thank you guys for all of the input.