Provided you know for sure that the ball joints, tie rod ends, drag link, pitman arm, idler arm, control arm bushings, are all good, I would then have someone sit in the car and slowly move the steering wheel back and forth while observing the movement of the steering shaft to the movement of the pitman arm. If there is excessive slop there you'll probably need a steering box. If your rag joint is original I'd replace it regardless. That rubber piece in there does deteriorate with time and exposure to engine heat.
Another area to check is the trailing arm bushings. If those are worn out that will cause the car to grab those ruts in the road.
Alignment is critical in a properly handling Corvette. Most shops don't spend the time to properly set up a C3. If you change any suspension component on the car you'll need to find a shop that will spend the time to align it.
I had handling issues with mine after redoing the suspension. 2 chain shops aligned the car. It was never right. Then I found a local shop that specializes in Corvettes. It took them 8 hrs. to properly set the car up. It was expensive but the car goes straight down the highway.
If your steering box is worn out, do not buy one of those cheapo units on "flea bay," most of them are junk. If you need rag joint, I think a may have one around the shop. If your interested send me a PM.
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GEN III 5.7L "LS6" Engine swap
TKO500 5 spd.
3.54 Dana 44