As far as I know your car will take either oil but the Mobil 1 is recommended as per the info in your owners manual kit. I really don’t think it would be a big drama putting in the Dexos on this oil change to get past the break in change. At least you could enjoy your car.
It if was me I would have that done “gratis” by the dealer and do a short change to Mobil 1 after a while. That’s the one that would be counted as your free break in oil change. Then you still have the 4 free ones left.
Any decent dealer would do that for you. But it seems this dealer is taking advantage of your situation.
This dealer must not sell many Corvettes. They clearly do not understand the corvette customer.
I pull into my dealer any time unannounced and instantly get my oil changed with Mobil 1 in the lube bay. Done it on 3 corvettes now. Never an issue. Plus they clean the car inside and out for free before I leave.
Hope you get somebody there to treat you properly as well. You bought a $100k car not a cheap ass mini-van.
PS: we are glad to have you here.