Subliminal shudder, possibly from the engine?

The miles listed above are the original miles on it.
Okay, we're talking about a car that looks like new, but is a classic ride based on its age.

The issue: I like to call it a 'subliminal shudder' during driving in every gear and at all speeds if engine and transmission has warmed up to their working temperature.

When you cold start the engine, the rpm jumps up to maybe 1,500 RPMs (don't have a rpm gauge in the dashboard) but comes down to maybe 800 RPMs within 3 seconds. This seems to be normal to me, because I had an '88 Olds Cutlass Supreme a few years ago, which is the same car, and it did this, too.
However, I put it into the overdrive position and start driving down the road (city limits) everything is fine, it runs smooth, accelerates as it should and there is no shudder. After 2-3 miles on the road the shudder starts and stays, so it's an issue that's just present when the engine and transmission has reached its working temperature.
So, the issue can't be generated by the really old factory tires, bad unbalanced brake discs or bad suspension parts (I guess).

What has been done until now:
First of all, I did an engine oil swap, new air filter and spark plugs, wires and the three ignition coils. I also cleaned the throttle body, but the issue is still present.

Just for your information:
There was (is) another issue: the car went off during driving after just one mile and won't came on when the engine had died and when I tried to fire it up again. It seems to be an issue with the charcoal canister or the lines that running through it, because when I opened the fuel cap, I could hear an inflating noise from the gas tank. I solved that on short notice for the moment, because I don't screw the gas cap completely down, so there is no vacuum build up in the gas tank anymore. By the way, the canister purge valve is working fine.

Back to the main issue: the subliminal shudder.
The transmission oil is really bad, this will be swapped next, along with a new transmission filter (parts have been ordered). But I don't think the shudder is transmission related.

There're are some ideas left in my head:
Bad/clogged fuel filter and/or fuel pressure valve? - No I don't think so, because it get enough fuel at highway speeds and long uphill roads
- bad oxygen sensor? - No, there is no SES light on (I checked the bulb and pulled codes from the ECU - No codes and bulb is fine, too.
- bad motor and/or transmission mounts? - Mabey, they're ordered and will be swapped soon.
- bad MAF sensor? - No, don't think so, because it will light up the SES.
- clogged catalytic converter? - Not sure, maybe, but then the issue should also be present with a cold engine, I guess.
- bad/clogged EGR-Valve? - It's an option, but will try to clean it first.
- bad/clogged PCV? - Don't know, I never had a bad PCV at one of my cars.
- bad intake manifold gasket? - Yes, that seems to be an reasonable option, but at 30k miles? - Mabey everything is possible.
- bad vacuum lines? - That could be also an option.

Feel free to brainstorm with me to solve the issue. If you have further questions, feel free to ask me. If I forgot something along my list, give me a soft kick.

Many thanks