While a Dana is going to hold up to slicks and a glued track, your going to notice the heavier rear end while on the street. It’s not going to handle as well. Usually the weak spot on an 8 3/4 is that the housing flexes and that can be solved to a point by bracing the back side, but that may not be your problem. Race duty axle’s may solve your problem. A Chrysler 9 1/4 rear axle while still is heavier than an 8 3/4 rear axle may be an option.
It’s always a compromise for a street/strip car. Either you give up street manners for racing durability or you live with parts fatigue while racing for street manners.