Slow4dr has it right on.... unfortunately being that the front subframe is essentially thin sheet metal and usually on cars these days that havnt been redone they are also usually rotted out.
The front geometry and strength on the 64-70 leaves alot to be desired by todays standards. that is why you find more complete subframe conversions that you will simple bolt on upgrades. With the simple cheap upgrades, you can get the car to have better manors however you cant cure the nuances of Ford's original design. That takes a crossmember, subframe or if your want to go all out a complete chassis replacement.