Second undergraduate versus masters with qualifying year I was a bit unsure whether this question belonged here, but after finding many questions requesting advice with respect to mathematics studies I decided to go ahead.

Over the last year I have developed a strong interest in mathematics and would like to pursue it at the university level. The long-term goal is graduate studies. 

My original intent was to first pursue a B.Sc in mathematics. I had met with the undergraduate coordinator at a university I would like to enrol in and he recommended that based upon my background that I may be better off pursuing a masters degree with a qualifying year comprised of advanced undergraduate courses.

My background is: 


Degrees: B.Comm (Economics), M.A. (Economics)
Mathematical Courses: Business Calculus, Mathematics for Economists (includes calculus, linear algebra, set theory, optimization, topology), Introductory Statistics, Econometrics
Research Experience: Four RAships, two upcoming publications (not in mathematics)
Self-study: Calculus (Stewart), Linear Algebra (Strang), Currently working on: A Course of Pure Mathematics (Hardy)


I would like to ask that given an individual with a background in a quantitative field, what are the pros and cons with pursuing either of these options.
If possible, avoid the 2nd undergrad. To see if possible, pick an online copy of a typical textbook, level advanced undergraduate/graduate, and browse it for fun, and do some of the early exercises. Examples: Artin: Algebra; Munkres: Topology; Spivak: Calculus on Manifolds (or more advanced; Guillemin &amp; Pollack;: Differential Topology); or better yet, browse whatever the curriculum of your chosen university indicated for this fall semester as text books. It doesn't have to appear easy, as you are supposed to learn it; and learning math is hard, no matter what your future classmates will falsely claim: most of them struggle too. But it shouldn't terrify you either.