I'm wondering if the tire shops you called understand the MINI's runflat tire technology. Sounds like they are assuming it is the type of tire that has a gummy inner liner that is designed to immediately seal the tire and prevent it from loosing air when punctured by something such as nail or a screw. (When I told my neighbor that my Cooper S has runflat tires, he said no big deal, his Dodge minivan has them, too. But he was thinking about the self-sealing technology)
You may need to tell the tire shop you tires are just like the late-model Corvette's run flat tires that are designed to be drivable without any air in them at all.
+ 2002 MINI Cooper S - Dark Silver / White roof, Sport, Premium, Lapis blue leather
+ 1965 Mini Traveller - Tartan Red / White roof, 1275, Cooper S discs, fully restored/renewed
Sounds like you need to find another tire shop, or a MINI or BMW dealership. Seriously, if they don't know about the run-flats they'll likely not have the equipment or training to properly remove and install them without doing damage,
They shouldn't have any goo in them, as others have already pointed out.
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