I have roughly the same issue with my '99 Sierra 2500 6.0, 304,000kms. I rarely drive it (paid $2,500 in 2012 with 283,000kms), so I don't spend a lot on it. It was running terrible for a while where I couldn't even pass anyone on the highway as it would just bog down completely (i.e. put me over the steering wheel). I did the simple stuff first: new plugs, fuel filter, air filter (and cleaned the giant mouse nest out), cleaned the MAF sensor (with MAF cleaner), and checked the throttle body (it was clean). The plugs and fuel filter made a HUGE difference to the point that it now runs fine on the highway, no problem passing.
The issue now though is that it runs about the same as it did when started up (cold)...bogs down so bad it barely moves for the first 30 or 45 seconds, then it 'catches' and runs fine from there. Idles a little rough, but not bad. It does this 100% of the time, worse in the summer (I live in Saskatchewan....+40C summers, -45C winters). However it will intermittently do the same thing when I shut it off and restart (hot, i.e. in a parking lot when waiting for my wife), chugging and bogging until it 'catches' again.
I have always had an engine light showing O2 sensor, bank 2, rear, so I replaced that one and the light just came back. This was several years ago. I read that the downstream ones have no effect on how it runs, so I didn't worry about it. The engine light has since gone out (about 3 months ago) and hasn't returned. Still runs exactly the same.
I do have exhaust manifold leaks, but they aren't bad. I haven't checked the fuel pressure, but I guess I could do that on startup. In my experience though a fuel pump usually just dies, but it seems maybe these GM ones can limp along forever? I was also thinking it may be the catalytic converter, but that seems like it would be an always thing, not intermittent like this. I bought a temperature sensor (cheap, GM genuine, $19) and will try that, but I don't want to start throwing parts at it.
Any ideas?