I don't think having 3 piece is a good idea to begin with you are just making it harder on yourself and it will be where the slingshot fails if it does. I could recommend longer thicker pins and two part epoxy as adhesive if you want to keep doing it that way or some sort of scales that connect all 3 pieces together plus some pins.
Yes but that connection is still a weak point you can try it and put a thick pin in the middle. But overall when making slings in my opinion is better and safe to have one solid piece of wood unless you have a solid inner core of some sort like aluminum then you can put whatever combination of wood you want on the outside glued with two part epoxy and clamped down for a really solid connection
I would slap a multiplex backing on it and shape it down so the feature woods dresses the multiplex. Either that or use a core and another scale but that would make it very thick to shape down. IMO the plywood/multiplex backing would be the easiest augmentation. You do need to clamp the parts together when gluing to get good fusion between parts (shouldn't rely on tape). You also need to ensure that the parts to be mated are good, flat and square to each other for a good joint. Looking forward to seeing your completed frame!
unfortunately this slingshot will never sling. but that's OK i learned from it and the helpful guys on the forum. My next project also not have a solid core (don't hate me, i'm just stubborn) but will have a cross grain lamination in order to insure that it is basically a board. Plan on using orangeheart, Yellowheart, wenge, Cedar, Tulipwood, and red oak.
If at first you don't succeed............. Try something harder!