I think Backdraft's have a strut style suspension in the front although I could be wrong. If they have a wishbone style front suspension like the SPF cars, the ball joints can introduce this type of vibration. Cobra Valley offers a pair of replacement ball joints for SPF cars that they call Hi-Performance Adjustable Ball joints to correct this sort of problem in the SPF cars.
As others have already suggested your tires could be culprits in the problem origin also. A bias ply tire can flat spot and also produce steering vibrations until they smooth out again.
The play in the steering wheel might be attributable to wear on the rack and pinion steering. Most R&P steering systems provide for some adjustment to compensate for wear. The other thing that could produce steering play could be steering u-joints that are beginning to fail.
Lots of stuff to chase down. Aren't these cars fun to own?
Ed