Here’s the thing, it could be, and most likely is, a case of a set of bad clutches and band, or it could also be a case of a torque converter with a bad set of hiccups. I honestly think it’s the first.
To explain, when your Silverado is revving to get into gear, a whole series of things happens in the transmission from the torque converter setting up the right flow through the valve body and gearing and then to the clutches/bands, the final stop before the tranny engages (like a manual transmission’s clutch plate/friction plate linkage).
I think that one set of clutches is definitely on the way out and the bands that work with it are also pretty sketchy, too. (They’d have have to since they have probably been working together since you put the truck on the road under your ownership.)
I don’t have any reason to think you have done any major work on the transmission because if you had had the work done, then I think it would have been in your complete description of the problem.
Of course, you can’t rule out the torque converter angle simply because a hiccuping torque converter may act just as you describe.
Have your technician take a look at the transmission to see what else may be involved. I think you’ll find that one or more of the problems I described is affecting the transmission. And, since the transmission will be open so you can have it diagnosed, have the technician obtain a rebuilt transmission, if you plan to keep the pickup on the road. I know it will cost about $3,200 with labor and all. But, once you have spent it, you’ll have a pickup that’s ready to do another 200,000. And, you won’t have to spend all the money that a new pickup requires (take a look, they’re not cheap!!).
Seriously, do have the rebuilt dropped in as I think it’s your best — and only — logical choice.
Let me know what happens, please, as I really do want to know.