I work on a fleet of Fords and experienced the same issue on a 2000 E-150 with a 5.4L V8. After replacing the coil pack for cylinder #7, the problem disappeared. To diagnose, swap the #7 coil pack with another cylinder's (e.g., #8) and check if a P0308 code appears. If it does, that confirms a faulty coil pack. Even if the misfire occurs on one cylinder, a bad coil pack will show up regardless of which cylinder it's installed on. This is often more reliable than EGR valve repairs in this case.
I work on a fleet of Fords and experienced the same issue on a 2000 E-150 with a 5.4L V8. After replacing the coil pack for cylinder #7, the problem disappeared. To diagnose, swap the #7 coil pack with another cylinder's (e.g., #8) and check if a P0308 code appears. If it does, that confirms a faulty coil pack. Even if the misfire occurs on one cylinder, a bad coil pack will show up regardless of which cylinder it's installed on. This is often more reliable than EGR valve repairs in this case.