Like Jeff says you are going to have to gain control over your rear suspension.
Your two semi-elliptical rear spring suspension has not changed since it's use with the horse and buggy and is named Hotchkiss for a French automaker who first stuck a tube driven live axel under the rear of their first automobile made around the turn of the twentieth century. It has not changed because it is the cheapest suspension system that works (we got away from chain drives as the speed got above ten miles an hour).
The disadvantage of using springs to both hold up the car and control torque is that it can not do both without offering a very harsh ride (which most car owners are not to found of for some reason). For this reason the factory compromised on the spring rate. When this suspension first came out in the 1967 Camaro the factory installed a trailing link on the passenger side to control spring wind up. In 1968 when the Nova was introduced and the number of cars using the same Camaro rear suspension went from a few tens of thousands to hundreds of thousands of cars the factory dropped the torque arm. To “help” control wheel hop they instead moved the passenger side shock from the back of the axel to the front of the axel.
Everyone who ever bought a Camaro that I know of back in 1968 or ’69 bolted on a set of Lakewood traction bars to control wheel hop because the staggered shock doesn’t work with a hot V-8. Cal-Trac torque arms will also work to control engine torque but unless you are making your own they are more expensive that a simple steel tube that rides on the front spring eye.
My 69 Camaro has Pontaic Firebird rear diff with factory traction bars, (2) with staggered shocks. it is almost impossible to spin rear tires from dead stop...even at drags with street tires (dry) they hooked very well...traction bars will help alot. j
The shaking you are currently experiencing without any form of traction control is wheel hop cause by spring flexing. Once that has been solved you shouldn't run into any shaking untill your power goes up enough to ball up a drag slick on a well prepared trac (one covered in rubber cement). If you think spring wind up is bad wait untill your first incident of tire shake; it'll rattle out any loose fillings you may have.
The universal bar will work but a bar specific to your car make and model works much better. The snubber should be directly beneath the front eye of the spring and not in contact with the spring at any other point or you could break the spring. I would buy a Competition Engineering competition leaf spring traction bar number C2101 if it were going under my car as they are going to solve your traction problems.