Adjusting the tension of the pedal did the trick, just easing off a little was enough to smooth it out again.
Unfortunately in my curiosity, I adjusted it too loose and the nut and other pieces holding it in place fell off, so I ended up taking it apart and reassembling the pedal. I took some pictures of the process so if anyone is interested in knowing what things look like under the hood I can share.
I was able to reassemble it and it's back in working order with no ill effects (and no more squeak).
For the curious, holding it all together are the following components
1 bolt
1 nut
1 metal mounting piece (to hold the nut against the mouting posts)
3 thin white plastic washers
2 thick white plastic washers
2 metal washers
1 black mount (to screw into the frame)
These components run through two mounting brackets on the pedal, and a tube mounted to the frame.
I'd love to know if I got the pieces back in the right place (since things started coming apart when everything was still encased and non-visible). I put it back together as:
Bolt -> thin white washer -> black mount -> thin white washer -> bracket -> metal washer - > thick white washer -> tube -> thick white washer -> metal washer -> bracket -> thin white washer -> metal mounting piece -> nut