That's an excellent lesson, definitely very helpful.
I hadn't thought of that approach to the root position for major and minor (I am going to have to add these shapes to my left hand's vocabulary as well now
); I normally have two notes on the 5th string rather than on the 6th string, like this:
Major (root position):
|----------------------9--12---------------------------|
|-------------------10---------------------------------|
|----------------9-------------------------------------|
|-------------11---------------------------------------|
|-------7--12------------------------------------------|
|----9-------------------------------------------------|
|-10---------------------------------------------------|
Minor (root position):
|----------------------8--12---------------------------|
|-------------------10---------------------------------|
|----------------9-------------------------------------|
|-------------10---------------------------------------|
|-------7--12------------------------------------------|
|----8-------------------------------------------------|
|-10---------------------------------------------------|