Scrambing into a spot is generally pretty tough as there are really only a couple spots open most years after the match.
That being said, a lot of spots (more than you or most people probably realize) tend to come up during the year. If you go ahead and do your internship, you will be eligible to take any position that starts in July, when your internship is over (MS IV's can't take those spots as they need a year to complete their internships).
In that kind of situation, programs are as interested in finding a candidate as much as the candidates are in finding positions. This has gotten a lot of people a spot through the years (out of the match), particularly at places that open up in mid-year (in recent memory, Moffitt, Mayo Jacksonville, UT-Southwestern, and City of Hope in CA have all done this out of the match when their programs were initially accredited) as well as places that end up adding spots to their existing program (IIRC, Utah is a program that comes to mind).