Never ran skinnies but I've street driven drag radials many times. Over the years I've had a few fairly powerful setups and drag radials are/were the best option imo.
My experiences are as follows:
Nitto 555R- Nice street manners, still has a relatively stiff sidewall so it tracks well down the road but it's the least sticky DR. In fact it's really just a soft street tire imo.
Nitto NT05R- Another DR with a stiff sidewall that has great street manners. Sticky tread, my favorite DR for highway driving. Nice ride and does just fine in the rain provided the driver realizes there are limitations to a high hp car in the rain.
M&H- These were always the stickiest tires but the soft sidewall results in a little drifting at highway speeds. I've had them in a few sizes and both were the same at highway speeds. Never trusted them enough to dd with them.
Goodyear- I don't think they even make DRs anymore. These were 275/60/15. They didn't drift at highway speeds, rode great, nice tires but not something you would want to throw into a corner.
My take was that I already had so much money into the car why not run drag radials provided they were safe? I always felt they were safer than regular street tires during the warm months, they didn't break loose as easy as my "summer tires".
My suspension setup was fairly simple. LCA, UCA, softer rear springs, and a full length axle brace. My approach to my mods has always been that the car has to remain comfortable enough to dd. This is why I took a tubular k member off after 3 weeks. It made the car far less comfortable on the street and my car will always be a street car.