Asking an external professor for a feedback on my BSc. thesis
Look for other magazines that don't require such a letter.  (Do they all?)
Find a professor that you can talk to. Or a postdoc.  Or a visiting scholar.  Some won't give you time of day, but some will be OK for a conversation.  Then maybe talk about what you've done that was interesting.  (Make some notecards and then be able to show/talk about the topics on the board.)  Keep it a little lighter than "read my manuscript".  That's a little leaden to be expected to read amateur work.  But a meeting where you are able to say interesting things like 

"lots of people want to have geometric interpretations of analysis and say that is novel, but they most likely think in areas or volumes.  I like to think in decision trees and nodes.  It's not really novel, as Russian authors from the 50s like Guestanovitch have written this way.  But it's kind of rarely seen nowadays."

[Made up example...I don't know analysis...but you get the drift.