Misfire cylinder one

On a long highway trip car had errors about traction control. Reduced engine power on dash. Car would not go fast. Brought to a GM dealer and they changed the throttle body. This was done with one from O'Riely as no OEM was available. Continued highway trip. Roughly another 750 miles. Once at destination car started to misfire. This was intermittent. Brought to GM dealer. Codes for catalytic converter and misfire on cylinder 1 and 3. Cleared codes. Only code remaining was cylinder 1 misfiring. Hundreds of times. Car was at shop for 3 weeks with no resolution. They changed the coil on cylinder 1 and all 6 plugs. Numerous tests were done and they were stumped. I was instructed to drive the car until it worsened. So I did and it did not really get worse. Brought to another GM dealer. This dealer said they pulled the top off and said it was full of sludge. Told me I needed a new motor. The total quote for the car was 14,000.00. They also tried to sell me a new car. Lol Therefore, I feel that was a complete waste of my time and money. Another $800.00. I then decided to try an independent shop. They had the car for roughly 2 weeks. No resolution. They are leaning towards an injector but are hesitant to go ahead as they are aware of the $1,600.00 I already spent on the issue which does not include the throttle body repair. Now I will describe the misfire. If I start the car and drive without stopping for more than a red light it does not misfire. Once the engine warms up and I say go through a drive thru or stop for 10 minutes or so with the engine on or off the misfire starts. I do not feel a misfire at idle at this stage or while accelerating slowly. The car however downshifts quickly even if I push the throttle more. It is like it cannot sense a load, I suppose since it is misfiring during this time the engine can't produce one. I can accelerate really slow and drive the car fine and not feel the misfire. If I try and push the car a bit more the misfire is very evident. The car jerks and will not downshift unless I really push the pedal down. If I put the shifter to manual I can get the rpm's up and the car will go and accelerate. The engine power does surge as if it is still misfiring however with the higher rpm's I think the rest of the cylinders can then power through. During the misfire the car is harder on gas. I do not smell anything. There is no smoke. Again, if I drive from cold without stopping long, the car goes like a bat out of heck even after warming up. The odd time I would feel a slight hesitation but no jerking or not much reduced engine power.