You're asking about using R7s for mixed drag and street use I'm assuming? I'm speaking strictly from my armchair as I've never personally run any of these tires, but here's my 2¢ based on what I've heard/seen elsewhere.
For drag: R7 is probably not the tire you're looking for. They're designed for road course use and need to be pushed for a lap or two before they get grippy. Hoosier says you want to measure temps in the pit at 180-200°F, meaning you'll need a little higher than that on the track. I might be wrong, but that seems to be a bit higher than you can heat the tires thoroughly with a burnout. An A7 (if you can find them in that size) would be the better compound for temperatures because it only requires 110-140°. On top of all that, both the A7 and R7 have pretty stiff sidewalls, but if you're sticking with the 20" rim you might not be able to get around that one
For street: I wouldn't run an R7 on the street if I didn't have to. Sure it's got DOT certification so it's technically legal, but it's gonna wear the tire out very quickly and you won't be properly heat-cycling it from street driving. Because of that, you might have even less grip later in the tire's life even if you do get it properly up to temp. If you manage to get them hot on the street, you'll start throwing rocks and other road debris everywhere as well if that makes any difference to you. You're also probably gonna have a bad time if you get caught in the rain with them.