Stuck nut

[lowercanada]

Problem....4 inch spread faucet on a deep, wall hung lavy has the black plastic "wing nut" stuck on like white on rice. I can't pop the sink off the wall because someone ran a tiled backsplash down to the back edge. I've managed to get some penetrating spray into the area (via the drain lift rod), but no joy. Tried grabbing one of the "wings" with small vice grips, to get a better grip....broke the wing off. I have an oscillating saw, but I think it's either not going to fit up there, or be too hard to position it just right. I've thought about a Dremel and a bur bit...lot smaller than the Fein tool, but still awkward. Thought about heat....either heat gun or open flame. Maybe sharpen a piece of steel long enough to get up in there to a chisel edge and banging away.
What do you folks think is the best bet?

 

[Breplum]

no such thing as best bet.
oscillating tool is good when it fits
we have winged nut removal tools
heating up a long-enough sharp metal piece to red hot and melting the nut
penetrating oil is totally worthless.

 

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[lowercanada]

no such thing as best bet.
oscillating tool is good when it fits
we have winged nut removal tools
heating up a long-enough sharp metal piece to red hot and melting the nut
penetrating oil is totally worthless.

Heating up a sharp piece of metal....didn't think of that, sounds like a winner....thanks