The diff is a big heavy chunk of metal to heat up, so if you have a highly localised heating method like induction or an oxy torch, you would be OK if you concentrated on the plug alone IMO. I'd certainly go down that route personally.
Before that though, I'd get a good cup brush on a grinder over the whole thing and see about getting a decently fitting tool into the plug and giving it a good whack with a hammer then applying a manual impact driver to it.
If that failed, I'd go for hammering in a bigger tool and trying impact again.
If that didn't work, I'd go for heat.
If none of that worked, I'd go nuclear and use a grease covered drill to put a hole in the middle and use a decent sized extractor on it, then flush the diff with thin oil before fitting a replacement plug and refilling.
If none of that worked, I'd remove the diff.
The first three options have worked for me in 99% of situations including seized drain/fill plugs. 2012 (L322) 4.4TDV8 Vogue SE, RSE, Fuji White over Arabica.
Previous V8s: BMW 645Ci, P38 4.6, P38 4.0, Merc CL500
Previous others: Honda x1, Volvo x7, Rover x6, BMW x6, Ford x1, Mercedes x2, Skoda x3, VW x2, Renault x2, Citroen x1, Mazda x3, Nissan x1, Audi x3, Kia x1, Fiat x4, Subaru x3, Austin x2, Triumph x2, Jeep x2, Hyundai x2, Lexus x1, Mitsubishi x1, Saab x2... and some others I've forgotten!
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