Nothing wrong with the rear end as I see it apart from the welds, how good those springs/shocks are is another thing. My back end was exactly the same on my old '71 340 s/strip car with stock l/springs which were clamped@the front, we installed longer r/shackles as you have (but used thicker metal) because I needed to raise the car up an 1" or so to clear my 10x28's. I bought some performance std. shocks and fitted 2" extensions, also fitted a pinion snubber and modified it for 1/2" gap to the floor., the car ran low 12's@108 dead straight. You do not need to waste money on sliders or a 4 link or caltracs, you could see my shackles in pics I have move forward around 4>6" on the hit as the axle bit into the track which is basically what sliders do except they are supposed to be more stable, I never had any issues with instability whatsoever and we raised the car more than you have it, the car ran straight and true and would pick the wheels a few inches.
Get the car to a decent track with prep where you can heat the tyres up and run it, get some slips and take things from there, no reason why that car shouldn't hook with what you have with a bit of sorting. If those are SS springs? you prob won't need the snubber, what I would say is to get some adjustable rear shocks, mine didn't have them and worked fine, probably would've been better.....If its a 440 car you may need some better parts/springs than you already have in the rear. You also need to look at the front suspension, make sure it moves freely and has at least 5" of travel.
