The 22nd would be Ok. You'd want to be at your selected spot for sinking around 3pm, if you're in my swamp zone (around Swansboro, NC).
The 29th would not be good, as the low tides would be around 07:00 and 20:00. If you were an early riser, the 07:00 might not be bad, but it won't give you much time for looking around, if you don't know where you're going.
If you don't want me to give you a guided tour, there are probably places that are closer to you that are also good for mudding. The spots I know of are on the White Oak River and nearby estuaries.