Acceleration Problem

I have a 1997 Buick LeSabre Custom with 115,000 miles on it.

So far I have replaced:
spark plugs, spark plug wires
air filter
fuel filter (broke the fuel line in the process, used a repair kit from NAPA to repair)
battery, fuel pump
UIM and gasket, LIM gasket and cleaned throttle body
Cleaned MAF sensor, replaced IAC valve, replaced TPS sensor, replaced MAP sensor, replaced PCV valve
Replaced water pump, coolant flush, thermostat, upper and lower hoses

Upon acceleration, there are certain uphill situations in which the car feels like it misses, that is, while the tach is steadily rising (slowly depressing gas pedal) it will suddenly drop from around 2500 RPM to around 1200 RPM. When this happens, the engine sounds like it is rumbling; the sound from the engine distinctly changes, and is much lower. As long as I hold the gas pedal steady, right where it is, the tach remains stuck at 1200 RPM and will not move, regardless of the terrain (hill flattens out, etc.) The only way to get the car to accelerate is to drop the gas pedal to the floor; then the tach will jump up and allow normal acceleration.

When cruising above 40 MPH (regardless of terrain) and holding the gas pedal in a specific spot (the same spot as the earlier situation), the tach starts to sway, it jumps up and down about 300-500 RPM from the current position (where the tach is when this happens varies). But as long as I hold the gas pedal in its current position, the tach will jump around rapidly. This sway is very rapid and extremely noticeable. Depending on the speed when this happens, the car will rock back and forth from the drastic changes in speed (normally around 5 MPH).

Both of these situations vary in severity and frequency, but are extremely annoying to deal with. Any help or suggestions are greatly appreciated! I have dumped a lot of time and money into this car, and I am completely out of ideas.

I would start by checking fuel pressure during this condition, also when did this start? I would also get a full scan done and look at misfire counts.

I already checked the fuel pressure since the pump was replaced; everything was normal during startup and run, and the pressure held properly after I shut the car off.

I do have a problem with the car and a low gas tank, I cannot let it get below 1/2 full (~8 gallons left). If I do, the car stalls braking/sitting on downward sloping hills. Sitting/braking while going up hills is never a problem.

I still have the fuel pressure gauge, but I do not see how it will be safe or possible to check things while the car is moving, plus the issues are extremely intermittent.

I have an Elmscan5 for reading OBDII codes and values with my laptop. There has not been a CEL, and all the values are within range. However, I do not recall seeing a misfire counter.

The car has already been to three separate mechanics, none of which could pinpoint the problem.

Keep the suggestions coming!

Sounds like the crankshaft position sensor or the ECM to me

Yup, could be or the balancer is coming apart also.

I'd check the EGR valve. Strange things can happen when they don't do what they're supposed to...

My 2003 Buick century V6 3.1 liter is doing the same thing. Its throwing code P0405. Sensor a circuit low. Guttles and no acceleration

If it runs funny below a half tank maybe your vent valve is not working properly. Sounds like an EVAP issue.

I already checked the fuel pressure since the pump was replaced; everything was normal during startup and run, and the pressure held properly after I shut the car off.

I do have a problem with the car and a low gas tank, I cannot let it get below 1/2 full (~8 gallons left). If I do, the car stalls braking/sitting on downward sloping hills. Sitting/braking while going up hills is never a problem.

I still have the fuel pressure gauge, but I do not see how it will be safe or possible to check things while the car is moving, plus the issues are extremely intermittent.

I have an Elmscan5 for reading OBDII codes and values with my laptop. There has not been a CEL, and all the values are within range. However, I do not recall seeing a misfire counter.

The car has already been to three separate mechanics, none of which could pinpoint the problem.

Keep the suggestions coming!

Sounds like a possible EVAP issue. Check the vent valve and the purge valve.