Unfortunately no, you might be able to heat it up with the iron and use the tip and the table to help even it out, but other than that, starting fresh is best.

Birdcaged isn't the end of the world, and sometimes adjusting the shape of the wire may be necessary to help it fit to the post, which will cause some birdcaging, but usually you do the shaping as best you can before tinning. Sometimes if a flatter shape is needed, tinning then flattening it out will work.

Glad its helping you.