Perhaps what I should have noted is that based on the reports (including where he's played this season and in the AFL), it doesn't appear the Jays think he'll stick at 2nd base very long...so play him (along with the other bench type players in Gurriel & Drury) all over the diamond and see if you can find a fit.
If the Jays see Biggio as a 2nd basemen (and their actions don't actually reflect their views), then yes, start him there the rest of the year and move Drury, Gurriel - even Sogard in LF/RF. Who cares.