Grant could have also commanded Murphy to construct the same defenses days earlier instead of the night before when the panic had started. He could have also left another 5,000 men there to help re-enforce it. He advanced too rapidly, leaving too much of a gap between his men and supplies. Other than the cavalry, much of his force was idling around Oxford and could have served a much better purpose guarding Holly Springs.
Other than some lightweight mountain howitzers I don't see how Van Dorn could have taken artillery, and I don't see how a small presence of artillery could have made his raid any more successful. I'm not sure of the Union artillery presence in Holly Springs on the 20th, but the CS forces could have easily taken anything convenient and used it. I think it was just too cumbersome, and the raid was moving at a total success anyway.
Sadly for the South, a large number of CS prisoners had been sent north only a few days before Van Dorn struck. Freeing these in the midst of such a raid would have greatly increased Van Dorn's strength, and helped carry off more Union supplies.
I believe the Holly Springs raid was the last significant event Van Dorn participated in before he was transferred to Tennessee. Despite the success at Holly Springs I believe Van Dorn requested this transfer in the aftermath of other previous criticisms of his actions as a general. He was quite a character, and brave to a fault, which made him too reckless for his own good. Still, one of the most colorful generals of the early war, and one I still enjoy studying.