I had to take off my rocker panels. The screws on the passenger side were impossible to screw off. I tried: liquid wrench, screwdriver, screwdriver with wrench, screwdriver with impact wrench (stripped slot on heads), vise grips, bolt removers (with impact wrench), hammer (tapped screws to see if I could loosen the rust), screw extractor (broke 2 drill bits and 2 extractors) and torch. Finally gave up and used a cut-off wheel to cut the heads off.

There are bolt threads sticking out of the holes. I have sprayed them with more Liquid Wrench. Any ideas on how to remove these? I'd like to put screws back in the same holes. I got hex head bolts instead of those infernal cheeseheads.

Heat them up till they are glowing red and use vice grips. If no luck you will have to drill it out.

Weld a nut onto them. The heat should help break the bonds that hold the bolt in, and you'll have a nice larger area to apply pressure to when you put a wrench on it.

--DD

Good idea, now I just need to find someone who can weld them! Do you think a local shop would do it? I might also have a friend of a friend I could ask. Any idea on what I'd pay someone? I have some holes in the rockers that need patching; maybe I'll have them do the bolts, then see if they can do the holes...

Heat them up till they are glowing red and use vice grips. If no luck you will have to drill it out.
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Do I put the vice grips on them while they are still glowing red?

I'm also concerned about catching the car on fire! I'm thinking the undercoating might catch. Am I wrong?

Just have a squirt bottle ready

Heat till red. Touch an old candle to the threads as it cools. The wax will wick down without evaporating like penetrating fluid. Use vice grips when cool (contracts). Try to tighten a tiny bit before you loosen. This will usually break it free.

Work they back and forth after the heat treatment.

...........leave in garage, set house on fire, then ........... ok, just fooling

When removing rusted bolts it is critical not to turn them too far in one direction as that puts too much stress on the bolt ( twisting it off ) or nut ( breaking the welds off ). Just work the bolt back and forth to wear out the rust.

I'd use a _new_ pair of real vise grips to grab what is left. A new pair will have sharp square jaws rather than worn ones found on used ones.

Liquid Wrench or other penetrant is fine, WD-40 is a miserable lubricant is is worthless.

If you heat the bolt, it will expand locking tighter in the nut so let it cool fully before attempting removal.

Bolt extractors are not as strong as the actual bolt, they mostly are for when a head is damaged but the threads are free. Bolt extractors are much harder than the bolt so drilling out a broken one is effectively impossible.

Post a photo of the "holes that need to be patched".
There could be corrosion inside the long, making removal of the screws impossible.

Drill out and retap. No one will ever know.