Can 'this' be used anaphorically?
e.g. He tried the door. This didn't yield.
I know 'It' would be standard, but is 'this' possible?
As a Brit, but not a teacher, I would advise as follows:
I would, as you say, normally use "It" in this context.
Where I would use "this/that" would be in the following context:
"He tried the front door. It didn't yield. He tried the back door. That didn't yield. He tried the window. That did, eventually, yield."
Hope this helps