IDK what power level you're at with that set-up, but I had a factory 03 Mercury Marauder that I installed an under hood roots Eaton/Magnacharger supercharger in, with an intercooler. I also installed headers, an aftermarket torque converter that yielded a 3,000 rpm stall speed, and 4.56 gears in the rear. I tipped the scales at the dragstrip@4,444 lbs with my 205 lbs of body weight behind the wheel and the half tank of 93 octane pump gas that I always ran both on the street and at the track with.
Without me in it, the curb weight was close to 4,200 lbs so the car was fairly close to being the same weight as what you're running. I had the car for three years, and I ran NITTO 555R drag radials on the street and at the drag strip, and I kept them@24 psi on the street, and@17psi on the drag strip and 17 psi worked the best for me with that car. I ran 12.0 to 12.2 second ET's, (depending on the air temperature) and consistent 1.6 second 60 foot times with that heavy tank of a car that it was, and on pump gas alone.
I had factory stock suspension both front and back, and I didn't even disconnect the front anti-sway bar, which usually is a no-no for drag racing. But I never had any wheel spin issues with those tires@17 psi. Of course driving on the street, I went through two pairs of them every summer, but that's the cost of better traction. Yes, I could still do burnouts with those tires from merely a dead punch from a standstill position in first gear, but when I wanted to get traction, I just walked it out of the hole from a traffic light in first gear, and I could then hit full throttle as soon as it hit second gear, and still avoid wheel spin. With the standard street radials, I couldn't even do that. You probably already know this, but I would highly recommend that you drive like an old granny with those tires whenever it rains. It wouldn't take much to hydroplane with them, especially when there are puddles. I always did a good pre-race burnout with them too.
What I also learned about the drag radials is that due to their soft compound rubber, they're much more sensitive to temperature changes than the harder compound rubber of standard street radial tires. On the street they provided the most traction when the air temperatures were above 60 degrees, but as soon as the air temps dropped below 50 degrees, I'd begin to notice a loss of traction during hard throttle inputs, and when the temps got into the upper 30's at night time, those drag radials would spin in first gear even with less than half throttle inputs, ( especially around turns). Almost like the street was wet, even when it was completely dry.
They're really good tires for street and strip use. You just have to know their limitations on the street. Also due to their soft compound, I never got more than 8,000 miles on a set of them. Based on what you said, my guess is that if you're making well below 600 HP under the hood, ( my heavyweight car made 475 HP) and you can't get the heavy weight vehicle you have to hook consistently at the track with the NITTO drag radials@17 psi, then your front and rear suspension needs work, and/or isn't set up correctly.
Do you have a front swaybar? And if so, do you unhook it when you're drag racing? What else do you have for FRONT suspension?