Hesitation, rich mixture, rough idle.

Have you checked the voltages at the O2 sensor?

You will have to get in with a live date scope and start checking all readings, you seem to have a good grasp on what is going on, but do not forget all the basics and do not presume something is okay. Check and double check, check base timing and timing advance, fuel trim, get your specs sorted and go check the system out from end to end.

Do not forget to test the sensors when the issue is happening. It sounds like the heat of a warm engine is changing the operation, heat sensitive issues can be a bear to find. One thing I do is get the engine into the "bad" area of operation, then cool down electronic modules under the hood one at a time. The cheap way to do that is to use the "canned air" sold in stores to blow off dust. Turn the can upside down and the actual 134A used in them comes out. Wear gloves and eye protection, it can freeze human tissue on contact!
You can also do that while testing a component.

You also mentioned that when you accelerate the rpm's rise but you do not gain speed? I would check the clutch, it might be worn enough that it slips enough to cause problems. Another thing would be to use an IR thermometer to check for brake drag. A bad brake line could cause a slow rise in brake pressure and cause drag. Depending on the brake materials the heat may not be bad enough to cause typical brake smell.