Mine had this same problem and ended up being a FRPS... Car would cut off fuel at 5200 and then fall on it's face and start bucking afterward, but would still start fine and run, got a code for the FRPS, swapped it out and was golden after.
Breaking up under acceleration probably means your going lean. You can severely hurt the motor by doing this so get it sorted before you boost up there again.
had a similar problem, mine would sputter or seem like it was cutting out as soon as I mashed the pedal (wot) in any gear any rpm. I did everything everyone above suggested pprv, plugs etc...etc still not fixed. I then changed the all 8 coil packs problem solved. Ford told me it ran fine driving normal cause of low voltage but at a higher voltage the packs were cutting out. just an fyi
Deleted the pprv. Now the bucking happens off and on. I am taking back to HP to check tune. My lap top crashed so no data log. I really appreciate all you guys help. I will let yall know the verdict.