It's a versioning issue!
If you look carefully, App Engine support was added to the master branch but the latest release is 1.1 and doesn't include it.
Instead of go get github.com/go-sql-driver/mysql
you need to manually git clone https://github.com/go-sql-driver/mysql
(master branch) into $GOPATH/src/
and then deploy to App Engine!
This comment from the author is what tipped me off and @Kyle's suggestion to try another driver (which worked) motivated me to re-read everything again - thanks!