There should be a small amount of flexibility in the dogbone (torque-strut), if that is what you mean by 'slack', but not a lot. It shouldn't move, like slide back and forth, in the bracket AT ALL. When GM re-designed the engine-mounts for these cars, they gave them a lot more 'slop' than they had in the original design. The drive-train virtually swings on two pivot-points like a rotisserie chicken, with the torque-strut holding it from pivoting. If the engine is jumping excessively, there may be something going on mechanically. For instance, if the idle is too high, it will jump, or if there is a transmission problem it could move a lot too.
Some people replace the mounts and/or dogbone with aftermarket polyurethane to stiffen it up, I have never cared much for it as I've seen too many of them break and the poly crumble out, and polyurethane is 'noisy', but some others have tried 'bolstering' their mounts with a liquid poly, such as that available from McMaster-Carr, an industrial supply distributor. Shouldn't need that with new mounts in a stock car though.
I think though, with new OEM mounts, the question for me is how much is it actually moving? Is it excessive, or just normal for the newer design, which is honestly quite a lot.