penetrants

Related question.
Plumbers putty or silicone to seal the drain. I suspect it doesn't make any difference.

Don't use plumbers putty on porous natural stone such as marble, granite of quartz, or on plastic such as acrylic or ABS.
Plumbers putty is oil based and can permanently stain the stone and degrade certain plastics.
Silicone's a good all around choice and also won't dry out over time like putty can.
 
Dean,

As mentioned, I'd use a dremel or oscillating saw to cut the nut.

Other thing, rather than working on your back and remembering to keep your mouth closed and eyes safe from debris would it just be simpler to pull the sink and fix this while its on a bench in your garage? A few minutes to pull vs. the PITA work environment squeezed under a sink. I assume you can remove the sink brackets, plumbing lines and then just pull the sink straight up out of the drain pipe if it's still attached.
 
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