The mustang continental spec tire is a 275/35/18. I don't know how much hp they run in that series, but I doubt it's over 600.

To beat him:
Put 335/30/18's on all 4 corners
get the center of gravity as low as possible while still maintaining a minimum travel
Ensure your suspension maintains a good contact patch in the corners
Beat his weight to power ratio across the rpm band you'll be working in
Upgrade your braking system to ensure no fade at threshold braking lap after lap

I have a similar yet lesser goal. Keep up with a C6 Z06 & a porsche GT3. I'll be running 275/35/18's on all 4, factory suspension geometry, a 3G Hemi, and 14x1.25 with viper calipers on all 4. I should be running in a few weeks and racing in a few months, so that should give you a baseline on what to improve on. Shoot, Tim's valiant and Peter's dart are both good cars to base a build off of with your goal in mind.