My take is the front spring shock combo is too firm. That combined with the lightweight of the car, open differential and the tire patch contact area. Wider tires don’t seem to help much in this scenario either because there winds up being less weight per square inch on the contact patch if there is no increase in overall weight. Stickier tire do help, along with softer, but not too soft, sidewalls on the rear tires and so does a locking differential. You won’t get hardly any weight transfer from front to the rear unless the rear tires do hook and start to push the car forward. In effect if the rear of the car is traveling faster then the front as in rapid acceleration from a stop, the front either goes up if the suspension will allow it, is pushed forward or it acts like a brake and speeds rear traction loss. If the front won’t lift and rear traction is lost kiss the entire weight transfer idea goodbye. The car also has to be stiff enough to transfer the acceleration force and not absorb it with body or frame twist. If the fine line between front end lift, weight transfer and rigidity is achieved the car darts forward with minimal lift or traction loss. This happens very rarely on any car.
As with just about any car reverse gear is the lowest so the torque multiplication is better but since there is no weight transfer onto the drive wheels(s) and a big drag caused by the weight of the front half of the car you get the hopping affect.
1st generation Mustangs are notorious for the same thing you are experiencing. One of the early drag racing tricks was to disconnect the front shocks to loosen up the front end and allow it to rise more and quicker to get the weight to transfer back before traction was lost under hard acceleration. I’ve tied it and it works.
Something else to consider is simply physics. Any suspension set up can be over powered. Take a look at a top fuel dragster; the engine can easily overpower the suspension and weight transfer. That’s why the driver can’t apply full power at launch and must work up to full power while the car is moving. Same reason why some cars with lower HP and torque out run higher powered competitors, more usable power to the pavement.