monotone min-3-sat polynomial algorithm?
3SAT is NP-complete.  Positive 3SAT (where all literals are positive) is in P, and thus presumably not NP-complete.  There is an even simpler algorithm for Positive 3SAT: set all variables to true.  That will always provide a satisfying assignment.

I can't comment on your algorithm  because it doesn't seem fully specified: you describe what order to make assignments to variables, but you don't describe how to choose a truth assignment for each variable.  (Should it be set to true?  to  false?  The question doesn't say.)