I’m going to suggest that this vibration is due to the same phenomenon as the death rattle - an oscillation due to the suspension geometry - and that worn parts aggravate the situation and added steering dampers are more of a band-aid, than a fix.
So I don’t think it is tires. I think there is one or more worn parts that is allowing the oscillation to amplify.
Death rattles are common on solid axles with a lot of camber. Yes, 1970’s Capri’s had it, too, and it was due to the way the suspension was designed. There is a rubber bushing that wasn’t stiff enough and replacing it with nylon fixed it.
But the common thread is worn parts.