Princess -- Stove Rebuild question

[Gone Kayaking]

After living with a less than strong flame on my stove, I've decided to give the burners a good cleaning. This involves unscrewing them from the bar that crosses the top of the stove....but they are really rusted. I'm looking for some good tips. It's a flat head screw.

First pic where one burner has the cover off (any ideas on how to secure this?)


Second pic