I like the idea of chasing with a tap first, and then bringing out the big guns if that doesn't work. Good info in the original post.
Do the threads here go all the way through the flanges on the frame? If yes, then try running the tap through from the back. It's less likely to further screw up the mangled threads at the front of the hole.
I'm trying to remember if it was this I screwed up a while back, or something else. Anyway, I've done that before (chase from the back end), but not sure it was here. Like UncleJohn, I use some screwdrivers sometimes for positioning, and may put in a bolt or two with just fingers and no grab handle in the way to get things lined up.
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