Some known issues that you may want to look into. Each of these can be the root cause of your problem. This will be long and I apologise, but I hope it helps.
The Fuel Pump - Ford had a Recall on this - seee below. A failing fuel PUMP gives bogging at anything more than about half throttle. As it fails, the pump cannot keep up with demand past 50%, the engine goes lean, and will cause the issues you are describing.
Originally Posted by RECALL INFORMATION
EXTENDED COVERAGE PROGRAM 04N02
Certain 1999 through 2002 Model Year Cougar Vehicles - Fuel Delivery Module
This program extends the coverage of the fuel delivery module (FDM) to 10 years from the original warranty start date of the vehicle, with no limit on the number of miles that the vehicle has been driven. This program provides replacement coverage, and is automatically transferred to subsequent owners.
VEHICLES COVERED BY THIS PROGRAM
Certain 1999 through 2002 model year Cougar vehicles built at the Flat Rock Assembly Plant from Job #1, 1999 through November 30, 2001. Affected vehicles are identified in OASIS.
REASON FOR PROVIDING ADDITIONAL COVERAGE
Some of the affected vehicles may experience engine hesitation, loss of power, surging, and other similar symptoms as a result of contamination of the fuel pump. Because the contamination of the fuel pump is progressive, it may ultimately become sufficiently blocked to cause the engine to stall completely. Although the symptoms noted above can occur under a variety of driving conditions, they are most likely to occur when there is less than one-quarter tank of fuel and/or when the driver is attempting to accelerate while making a turning maneuver (such as entering a highway through a cloverleaf) or while driving uphill.
If the customer informs you that their vehicle exhibits stalling, engine hesitation, loss of power, surging, or other similar symptoms, replace the FDM. There is no need for further diagnostics prior to FDM replacement. Owners are not to be charged for any diagnostics or repairs related to the FDM replacement.
Prior to performing service, tell the customer:
Ford will replace the FDM at no cost based upon the customer's description of the condition without performing any diagnostics.
That without performing diagnostics other conditions that may affect driveability, if any, would not be addressed by an FDM replacement.
That diagnosis and correction of any remaining driveability issues, if any, are the responsibility of the customer unless the vehicle still has remaining Basic Vehicle Warranty coverage.
That after FDM replacement, a road test will be conducted at no charge to determine if the driveability concern has been corrected.
This Customer Satisfaction program only covers replacement of the FDM.
Please note: It is not necessary to replace the in-line fuel filter due to this issue. Fuel filters should continue to be replaced at normal maintenance scheduled intervals.
Also note, the "some vehicles" means late 99-02 Cougars. The early builds with the return fuel system is not covered....but don't worry, those fuel pumps are not the ones failing.
Understand that the newly designed fuel pump will be available in late June. Be sure to schedule an appointment when this pump becomes available or else you will eventually be in the same situation again.
The new fuel pump is now available. Ford part number XS2Z-9H307-CA. Please be sure to get the update part installed.
According to Ford:
1. New pumps exist now but they are backordered.
2. Dealers can install a temporary pump for cars with real bad problems. Later, new pumps can be installed.
3. All this is covered under warranty. No mileage limit or time limit. Even if you're not the original owner.
Dielectric - You will need to have the dielectric grease on the plugs. If not you will damage the plugs and possibly boots. If the dealer has put the wrong grease on it they should be responsible to replace with the correct grease. Using the wrong grease will also cause issues and possible damage.
DPFE - If you are getting a CEL code "EGR flow insufficient" then replacing the DPFE will usually fix this problem. You will experience bucking, hesitation and stuttering under heavy loads or heavy acceleration.
Hope that this is of some help.