S&T and MFE?

3.5 HYP in Applied Math/CS, Junior. I've really become interested in fixed income trading, but I have no relevant work experience so I figure FT recruiting for S&T will be absolutely impossible. My resume looks really scatterbrain - some finance activities, some cs, ect.

Any chance of getting into a reputable MFE program? Do most/all programs require relevant w/e? In that case, this seems like a catch-22. How well do they place into BB S&T? Or should I just forget it? Thanks!

Also, does doing well on the Putnam help for applying to FI trading?

Thanks.