I have never used the slingshot cast but actually got the bow and arrow cast down pretty good early in my fishing career when I fished several tiny, brush choked streams a couple hour drive from my house. The rod I got good with is an eight foot, slow action Winston rod. I unwind maybe 15 feet of line and pinch it off at th handle with the rest unraveled by my feet ready to shoot, then grab the bend of the hook, put the rod parallel to the water and let it fly. I got to the point where I could shoot maybe 15-20 feet of line out under bushes and overhangs. I viewed it as a novelty cast at first but when I got effective at it, it paid off more than a few times and it was kind of fun. I'm going to give the slingshot a try though.
I would think shorter, slower rods would work best with the B&A cast. I found that when I used a stiffer rod that it whip the line around too much and cause problems. Fun stuff.