That’s what any troublesome project is, of course. And, as often as not, at least some of the losing steps make the problem worse, and you have to cope with that along the way.
In this case, replacing license plates. Nothing much wrong with the old ones, especially the back one, but in Minnesota they get replaced every 7 years anyway. Now, I think I’ve had these 8 years, but never mind.
Front one was easy; though it’s held on by big sheet-metal screws straight into the bumper (which is not sheet metal). But they still feel reasonably solid.
The right-hand screw on the rear one was easy.
The left hand screw, not so much. I was down to my next-to-last idea, before taking it in to a professional (and paying the “if you worked on it yourself first” rate I guess) on Monday, if nothing had worked.
- Big #2 Phillips screwdriver
No effect. Didn’t actually raise blisters on my palm. - #2 Phillips bit in ratchet handle
This gave me more leverage, plus separated pushing in hard (left hand) and twisting (right hand). Screwed up the head pretty good. - Penetrating oil
Not easy to get at where the screw entered the threads, screw head and plate frame and plate were all in the way. But squirted a bit in the general direction, and waited overnight. Then tried Phillips bits again. No go. - Screw extractor
Drill into the screw head, then thread the extractor in and twist like hell with a wrench on the end of the extractor. Broke the extractor clean off. Not aware of slipping and getting forces the wrong direction, but no doubt doing this with magic tools to keep things aligned perfectly instead of freehand would have been less likely to break anything.
Damaged screw head with broken extractor - Break off the plate frame
It was between the head of the screw and the plate, so removing it gave me more play and better access to where the screw entered the threads. Tried twisting the screw head with slip-joint pliers, no dice. More penetrating oil, now that I have better access (and wait overnight again). - Try turning the screw head with channel-lock pliers
This actually worked! A bit slowly at first, but I got the screw out.
(The next step, not used, was to try to file down two edges of the screw head far enough to give the pliers a better grip.)
New screws are stainless (had to replace the left one anyway, since I’d pretty thoroughly ruined the head). The threads are metric (M5), though, so the heads aren’t a convenient size. The adjustable wrenches will fit them, but that’s much slower than nut-drivers or ratchet sets.
Definitely cheaper than taking it to the professionals (one $5 Irwin extractor, broken; trivial amount of penetrating oil out of existing container). Considerably more time and annoyance, though.
[Edited 7/24/2017 to remove two bad photos of damaged screw head and replace them with one decent one. And switched to consistently label this large machine-screw as a “screw” rather than a “bolt”.]