Welcome to the handling characteristics of a GMT400! Lol!
Due to the amount of pivot points in the steering component design (IIRC, there's 8) any bit of play or slight wear in 2 or more of those components & the prob becomes amplified.
For instance, on my '97 right now, none of those parts are bad enough to warrant replacement, but all the small amount of play in each one, & the truck handles like poop! I have a fairly new steering box, too!
Go through the front end and make sure that the combined small amount of wear is not totalling up to a larger prob.
Check the rag joint.
Repack & re-set the wheel bearings too. Cheap & easy!
After that, get an alignment.
When you do, get the tech to set as much camber in as possible. This will give you a slightly heavier feel to the steering, but the truck will WANT to come back to center.
If the truck hasn't ever had a 'proper' alignment, it'll need the slugs knocked outa the upper control arm mounts. Doing that allows for more castor. Without those slugs knocked out, the truck is riding slightly on the outer edges of the tires. (Top out, bottom in) This'll cause the twitchy steering in the big truck ruts as you've described. Why GM never punched the slugs from the factory is beyond me!
Are you running larger/wider/heavier than stock tires? If so, get the tech to dial in a little more toe-in.
A truck, when it's not moving, is out of alignment. Not much, but it is. It's not until the truck starts moving that the drag of the tires will pull the front-end into the alignment spec that it requires for somewhat (It IS a GMT400, after all! Lol!) decent steering & handling. Larger/wider/heavier tires, &/or wheels, create more drag, & they'll pull a stock setting back too far, creating a wandering characteristic. (Toe out)
The specs for vehicle alignments have a plus/minus zone that the tech can work within.
But just because a Co. has an alignment rack, doesn't mean that they understand front ends. Anyone can learn how to set to spec as according to the book. And for the Average Joe, close enough is good enough.
Due to the design of these truck's steering, that doesn't fly. They need to be much more accurately set. And that includes being test driven. Over all types of roads & situations. Not just around the block. The shop must be willing to set & re-set as much as required in order to get it right. If it needs to be on & off the rack several times, well then, that's what it takes to get it right.
If the shop you go to refuses to to understand, or just plainly doesn't get it, move on to one that will & does.
The guys that I use specialize in doing track vehicles. They 'get it'. Even if they have to set the alignment slightly past the +/- settings in 'the book', if that's what it takes to get proper safe steering, then that's what it takes.
At the age that these trucks are now, they are separate individual entities, & the parameters of the stock factory specs may not always apply. Your neighbor may have the exact same truck, but his alignment specs are probably not be the exact same as your's.
Some alignment shops will only set front ends as per the the stock spec. They're not thinking of the vehicle as an individual that could require settings specific to that one vehicle.
Hope this helps!
Good luck!