Serious Front End shake

My 1970 Challenger has a really bad case of the shakes.
As I approach 50 MPH, the front end starts shaking badly and it gets progressively worse as my speed increases. I can really feel it in the steering wheel and you can see the entire hood shakingse I am afraid that the car will shake itself into pieces.

I had all four of the Rallye wheels balanced by two different places and to rule out bad tires, I even put new Radial tires on it. They are cheap tires as I did one of those buy 3 get 1 free deals from Pep Boys.

I went cheap on the tires because I plan on moving to a set of  Magnum 500 15" wheel from my current 14" Ralllye Wheels.

I personally watched the mounted tires spinning on the balancer and they were dead on perfect so I have convinced myself that it is NOT a broken belt in the tire  or a bent wheel issue.

The front end is all original and I plan on having it rebuilt with one of the modern polyuretahne bushing type suspensions. Something like the PST POLYGRAPHITE® SUPER FRONT END KITS. I have several reviews of different fronmt end kits in my Mopar Muscle Magazine issues

Before I do all this though, I am trying to figure out what could be causing such bad shaking and how to get rid of it.  Crawl before you walk before you run is my philosophy.

Can anyone toss some ideas around that may explain why the front end is acting like this and/or diagnostic tests I should be doing to figure it out?
BTW, my car is not a 'beater'. The restoration is  about 90% done accodring to my plan  and the car looks/runs great (except of course for that darn front end)

Thanks for any replies  

Worn ball joints, tie rod ends, pitman arm, idler arm, can cause the front end to vibrate. You'll need to get under it and see where the slop is. That's the 1st place to look.  

Dont forget the weel bearings also