I have actually found the answer
I restore to localhost using Kickstart and have always set the database type to MySQL, not MySQLi. The latest version of Kickstart only offers MySQLi (preferred) and MySQL (with PDO) - plain old MySQL is not an option. Not knowing any better, and since I'd never opted for MySQLi before, I chose the latter.
I have done another restore using MySQLi and everything has updated nicely, without any errors. I hope this information will be of help to someone else, and thank you for your assistance. Great support as always!