The ONLY reason your radials are not working now is that your clutch is simply hitting them too hard. Simple as that. They are spinning because the clutch knocks them loose before the car has a chance to transfer any weight. Soften the clutch hit and everything else will come together with far less effort. In the end the car will be faster with radials, as a bonus you will be able to drive them to the track. Far less expensive overall, and the car will be more fun as a true street/strip ride.

If you switch to bias slicks without softening the clutch hit, the added sidewall flex will give the car more time to transfer weight. You will end up with the kind of dead hook that breaks parts- too much clutch hit combined with "too much" traction. You will be forced to either reduce traction to minimize the bog or beef up the drivetrain to take the extra abuse. The car will also be super sensitive to air pressure and shock settings while you search for ever changing perfect balance between bogging and spinning. The fix usually ends up being an expensive adjustable clutch, which brings the added inconvenience of switching the clutch back and forth between street and strip settings.

You likely have mechanical clutch linkage like I used to have on my '70 Challenger, but here's something to think about...
I have a hydraulic clutch hit control system on my current car. It basically converts my conventional hydraulically actuated clutch into a 2 stage system- initially the clutch hits on a softer 1st stage for the launch, then when the transition timer times out the 2nd stage of full clutch clamp pressure comes in to lock the clutch up. Setup is very straight forward and easy to understand, and I can change the intensity of the 1st stage hit by rotating a simple knob.

A few weeks ago I was experimenting with a 10.4" Ram dual friction organic/metallic disc, combined with a Ram 2800lb diaphragm PP. Normally a dual friction disc combined with a 2800lb pressure plate would be a super aggressive setup, but this one has it's hit softened by the system mentioned above. The car has a 2.78 1st gear, 3.73 rear gear, and 28" M/T 275 radials @ 28psi. The transition timer for the clutch was set to 1.0sec. I fired the car up, drove a few miles from the shop to warm the oil up a bit, then stopped to make a hit. Dead cold 275 radials on a random stretch of chip sealed county road, zero rubber down with no burnout at all. The 4500 clutch dump produced a dead hook launch with a peak of 0.98 G's @ 1.02sec. When the 2nd stage of the clutch kicked in at 1.0sec, it knocked the tires loose and as a result the accel G's dropped to .72.

I later did basically the same routine, except this time I bumped the transition timer setting up to 1.5sec. This time a 4900 clutch dump produced another dead hook launch with a higher 1.22 G peak @ 1.8sec in, well after the clutch's transition point. That simple addition of 0.5 sec to the transition timer setting improved peak accel by .24G's, also got the car to 50mph about .625sec quicker. No other changes between those two hits, just that .5sec addition to the clutch transition timer setting.

Dead hooked radials from a 4900rpm clutch drop on a random chip sealed county road with zero surface prep and no burnout at all. The dual friction disc doesn't complain at all about the 1.5sec slip time that it takes to bring it all together on the zero prep surface.

Grant