Hey Scotty. 

I'm at my wit's end with this one. 
-  2014 Chevy Captiva
-  145,000 miles. 
-  Car starts every time, no hesitation. Good steady idle. Feels, sounds great! 
-  Pulling away the car feels slightly underpowered, hesitant, but drives well. 
-  Will buck at random, any speed. The RPM gauge will bob. 
-  When bucking, the car will stall if I come to a stop. 
-  When running fine, holding the accelerator at a speed, the accelerator will stop responding. I could let go or push it to the floor. No difference, the car is coasting. 
-  OR - pressing the accelerator will result in a compression breaking effect, slowing the car down. 
-  Then, sometimes, When then accelerator is failing, I will press the petal for no response for several beats, then the car will shoot forward as if its getting all the fuel at once.
-  Issues are much more prevalent when transmission is engaged to drive gear. Setting transmission to Neutral or Park may stop the bucking, car may return to good steady idle. 
-  No visible power drain. Lights (internal and external) remain steady and bright until the car stalls.  
-  Intermittent but reliable issue. I can't drive 5 miles without symptoms. 
-  No Check Engine Lights. No Codes. 

Troubleshooting: 
Cleaned the MAF
Cleaned the Throttle body 
Replaced both O2 sensors (bank 1 coded too rich, replaced both) 
Replaced the catalytic converter after a P0420 code after the O2 sensors were replaced. 
Replaced the fuel pressure regulation pump (on the cam)
Replaced the Coolant Temperature Sensor (it coded, caused a check engine light)
Replaced the ERG (started running Much better at this. Not fixed, but much better)
Checked grounds (all good - no electrical issues)

Next up
Fuel Filter and pump (both in the fuel tank)

I've been to 5 mechanics, 2 GM dealerships. I've had bad diagnostics, the run-around, and turned away because it doesn't have a check engine light. 
I'm looking for anything else I could check.