The only problem with the easy-outs is that they need a depth of at least the width of the hole, and that's if you're using the very tip.

I'm talking about the regular, tapered easy-outs... Snap-On and a couple other
large tool companies make some better ones, that aren't as tapered,
and have multiple sharp reverse flutes... they can take a bit more shallow hole.

If we're talking about a 3.5mm screw with a tiny head, it just ain't happening.

The idea to turn it into a flat head was the best, if you can get to it to do that.

Like someone else said, you may just end up trashing the mount here.

In the future... use better screws and/or better (or the right) tools.
I've been bitten by this one a few times myself