Personally, I never say "within this context."  I can't think of a time when I've heard it.  (Canadian context.)  It would make sense, though.  To me, it's a shift of viewpoint.  "In this context" means "In the context to which I'm referring."  The speaker could be discussing something happening on the other side of the world that does not directly affect him/her.  "Within this context" would seem to invoke a direct connection to the context.  It could be that the speaker is personally involved in the context or the speaker could be referring to someone or something that is directly affected by the context.  It makes me think of the expression "within the confines of" to indicate that what you're discussing is bound (as in restrained, constricted, "in prison") by whatever follows.

Thank you for the detailed explanation!