Thanks for that suggestion.  I could use a Thermapen to check the temp without stirring.  Another interesting development: As I was cleaning the pot from the separated batch, I saw the butter now solidified.  I mixed it into the remaining butterscotch, and it mixed quite well.  So I will try browning the butter, letting it solidify, then adding it after the caramel has been totally cooked.  I hate to abandon that wonderful taste/smell of browned butter.