I haven’t dove the U352 yet, but it is on my list of sites to dive. But being from NC and having dove at our coast numerous times, I can tell you that diving anywhere on our coast is a hit or miss prospect. Thunderstorms can roll in at any time and even if it isn’t raining, the wind can cause dives to be cancelled. I’ve been down for a weekend of diving before and get blown out one day and the next day be picture perfect. You just never know. But I would say Mid-July to Mid-October would be the ideal time of year to go. The water will be the warmest at that time.
As for visibility, it will always be better if you can catch the tide coming in. I’ve dove wrecks before where visibility was 50-75 feet when the tide was coming in, but the same sight had 10 feet of viz or less when it was going out. Our barrier islands along with the many rivers emptying into the backwaters can create a bunch of crud in the water. So check your tide charts for the Morehead City area and try to plan around incoming tide. Maybe you’ll get lucky and hit the trifecta along with a calm & sunny day.