Besides just tossing out the blower/gears option, which assuredly wouldn't allow you to keep up with a 5.0 but, factors aside from traction and driver skill, you'd walk away from one quite easily. A supercharger shouldn't be the only route to achieve this, per se.
You're off to a good start but, you have to factor some real world figures into this prospect. For instance...
A stock 5.0 has round and about 370rwhp with torque being not that far behind.
A stock 3.7 has about 260-270 depending on whether or not you have a manual transmission, heat, etc. Lets just assume you have a manual transmission and all other factors play in and you're smack dab on 270. Thats a 100rwhp deficit. Never forget that glaring fact.
Your torque will be significantly less, 240ish, give or take once again. The weight differences between the two vehicles are almost negligible but, they exist nonetheless. You're going to have to play that factor to your advantage as much as possible because frankly, you'll never overpower one all motor. You're going to have to out launch it, out shift it and out gear it. Of course, you're going to need to get your hands on pretty much all of the remaining bolts ons, also.
I've had several V8 Mustangs and I remember how smug I used to be towards V6's, also. Don't sweat it. Realize the differences from the get go and plan from there. There are several folks on this board who are posting some very respectable times with their 3.7 all motor. I'd wager to say that it would be very tough for the average coyote driver to keep up with them. Remember, when one of them scoffs at you for having a V6 instead of a V8/Coyote, the argument is moot. You could toss that silly argument out the door and continue to "one-up" each other all day long.
Take a good look at the sticky on the main page and what folks did to achieve their times. Work from there.