alright. i just recently had this problem. i guess it wasnt the problem that i couldnt get the screws out. it was the problem of not having anything for the screws to hold on to. what i would suggest is going to ford and paying something like 12 dollars to get this replacement part that basically reinstalls the two holes on the top to new. and if you choose, you can do the same with the bottom but not neccessary. the kit requires you to drill out the top two threaded areas with a 5/8in hole cutter. so it probably wouldnt hurt to drill out the screws if you were going to go this route. just make sure you do a clean job and dont break the plastic.
oh, and to answer the question about getting the screws from the bad. will require drill since they do not go through. there are just bumps in the back side where the screws would be...a design of the part.
hope this helps. let me know how things go.