Here is one other thought/question- seems like everything I have read thus far leads me to believe that even if I CAN get the screw ends out of the holes, there may be damage to the holes that they were stuck in (ie they were screwed so far down that it punched the holes out too big for new screws to do any good.).
But, correct my reasoning if it is wrong, wouldn't the fact that the tips are stuck imply that there is still a small enough hole diameter to "seat" the screw, it will just seat slightly lower than before the tip was broken?
To put it another way, the screw tip broke off and is plugging the hole- doesn't this mean that the hole is till small enough to seat a new screw? The "seated" position that I would need to find and then back off a few turns would just be slightly lower but will still provide a seal at the "seated" position?
Does any of this make sense?