It's amazing that they survived all that heat. I have a burn pile also and know what you mean about the different stuff that is burned there. It's not just cardboard boxes. Old computers, vacuum cleaners, garden hoses, etc. Stuff the garbage man won't pick up, but it's thirty miles to the county dump. I have to occasionally rake out the metal that doesn't burn. It's amazing how little metal is actually in most small appliances, stereos, etc. nowadays. It's mostly plastic now.
The plants should transplant easy enough. It will be good practice for "Name that Variety". You could start a new game show. lol.