A lot of new cars in that situation with limited slip and rear tires that wont fit the front come with a compressor and fix a flat.
I don't want to jinx myself but the two times I've had a flat the first time I had a full size spare in the trunk and called CAA/AAA to change it since i'm already paying a member fee. The The second time I was able to get enough air in it with a 12V compressor to drive home and then get a garage to fix it. Now I like keeping 12V compressors in vehicles just in case. Old truck, in winter at night. No way i was going mess around with the spare especially mounted underneath.