I am a clueless n00b, but I will offer this:
The screwdriver tip may be wider than the hole, so I would not try to push it all the way through.
You can punch the pin out from the other side.
Just buy a punch and a 4lb hammer.
I bet you can just smack everything back out from the other side.
I used to assume all hammers are the same, they are not.
A heavy $12 hammer carries a lot more force (F=MA)