Motor mounts are the usual cause...this is a very frequent complaint...fortunately there are some good answers. Original equipment motor mounts were made fairly well and the rubber part was hard stuff. Reproduction mounts aren't made to the same standards and can use a softer rubber compound that stretches more easily. Add more horsepower and torque and the weaker mounts give you "shaking" problems with manual transmission cars. Try a set of Lakewood Muscle motor mounts.
See
http://www.mrgasket/pdf/lakewood.pdf
Since this is a portable document format file, 755K long it will take some time to download and you'll need Adobe Acrobat Reader software (free) to read it.
These muscle motor mounts aren't that expensive. They have torque limiters built in so when the engine winds up at start, you don't get the clutch chatter from excess movement of the clutch linkage. You can do this yourself with your existing mounts. Here's two ways:
1. Remove the mount. Drill a 7/16" bolt hole through the metal, rubber and metal. Insert a 7/16" bolt through the hole thats 3/8" longer than enough to penetrate the motor mount. Cap it with a nyloc or toplock nut but do not tighten the nut down, rather leave about 1/4" clearance between the shank of the bolt and the nut. Your motor mount will serve to isolate engine vibrations but when the rubber tries to stretch more than 1/4", the bolt will limit the motor movement.
2. Strap the mount with steel cable. Wrap the motor mount with a loop of substantial steel cable (about 3/8" wire rope). Fix the loop with a professional compressed joint between the ends. You'll likely have to take the mount out, measure for the strap and then have the loop joined by a shop having the ability to join rope ends. (This is the way GM solved the problem on early Camaros). The rope loop should fit fairly tight when installed.
There's also other commercial alternatives such as TCP's custom mounts for early Fords.
See:
http://www.totalcontrolproducts.com/main.html
The featured item is on the main page at the current time. These aren't cheap.