It seems unlikely that the vibrations are due to the sub-frame mountings. Early cars had solid mounts and they didn't vibrate like that.
In fact, the superb steering response of the early cars was degraded on post-'76 cars when the rubber mounts degraded.
I have solid mounts on my 1964 car and have fitted solid ones on my 1990 Cooper. Never would I go back to rubber mounts, nor those horrible poly ones.
As above, you only need to drop the back of the sub-frame by about 3/8" to remove the top mounts and fit new ones.
Nick is right that your rubber cone springs look to be past their 'best by' date.