I would personally not skip the tires.
I had ten year old tires on my Lamborghini Diablo some years ago. Same story as everyone - low miles car with excellent tread left. I took a visiting friend out in the back roads around my house for some fun, touching 130 in places. After I dropped him off, toodling home at 55, the right rear suffered a catastrophic failure and completely separated from the sidewall. If that had happened a half-hour earlier, there's no question in my mind that the car would've been totaled and possibly me and him with it. No prior evidence of issue with the car or the tires, and proper tire pressure checked and maintained at every drive.
I bought my 2005 Vanquish S used in 2012. Had the original tires on it, which had great tread life left. The first few months I was disappointed with the handling of the car. Not nearly as sharp as I expected and it wanted to spin tires in many places where my old Testarossa would not. When it dawned on me to check the tire dates, I replaced them immediately. The car was transformed. New grippy rubber gave me the car I knew I had paid for.
I know that things add up in a hurry, and those of us (myself absolutely included) who buy depreciated cars that might otherwise be either unobtainable or unwise, are tempted to save where we can. But tires are the only thing connecting your six-figure car and your priceless butt to the pavement. If it were me, having been nearly burned badly, I would skip everything else first to do the tires. Just my $0.02.