Well your not alone. I've been down this road way to many times and I have found the winning solution. It's fast, easy and your going to think why haven't I already thought of this. Or maybe you have!
Step 1: Getting a Grip on Things
Well I have seen many DIY videos telling me how to get a stripped screw out.
Strip screw head!
Yell words the kids are not suppose to hear
Apologize to the wife for being such a bad person in front of the kids
Use a Dremel with a cutting disc to cut a groove through the center of the screw head.
Put a band-aid on your finger you just cut while yelling more obscene words.
Find a flat head screw driver, hopefully you didn't through out all your grandfather old tools. Do they even make these things anymore? I'm just kidding guys!
Spend 30 Minutes trying to remove it then switch to the vise grips to finish it off. Be sure to take breaks and use more obscene words.
Get the same screw and after it strips again do steps 1-7 again with more bad words involved.
OR YOU COULD!
Step 2: Speeding Things Up!
You will need you screw head to be sticking out about a 1/4" from your work surface.
(If you don't have this clearance you may need to cut a slit in the head of your screw so a flat head screw driver can fit. Then back the screw out to about 1/4" clearance from your work surface.)
Take a standard drill without a bit. Open up the chuck so the head of the screw or shaft of the screw (if no head is present) fits into the chuck.
Now hand tighten chuck onto screw. Get it as tight as you can.
Put drill in reverse and slowly back screw out.
Celebrate while your grandfather tries taking out the other stripped screw the old school way!
30 minutes later show him how to do it the easy way!