Ah, The Narrows! Good memories of a great hike. I did it over 10 years ago. We were going to backpack it and spend a night, but we had taken mountain bikes, and one in our party didn't feel comfortable with his bike locked up a night at the car while he was out on the trail.
It was crazy that we had hauled backpacks and gear from home, but didn't use it. But the dayhike worked out just fine.
To answer your questions: Unfortunately, there is no middle ground. It is a long (> 1 hour) drive to the trail head. We hired a shuttle service with a rattly van -- rattly because the gravel road goes for miles. We hiked it in September, since that was statistically the best time to be free of any storm/flood issues. And water level was lowest, so hiking was easiest.
The NPS controls the permits tightly, day hike and overnight. Overnight sites are assigned. When we went, you could only get them the day before in the park. I got up super early to make sure I was first in line (at 7 AM I think) to get the next day's permits. They will not issue any permits if weather forecasts are questionable. (You don't want to be caught in some of that hike if there is high water.)
As for the hike, you wade in water about a third of the distance. Some of the river bed has larger (pumpkin sized) boulders, so you are searching for good footing with your feet. Hiking poles are a big help. I wore old hiking boots for the hike and retired them afterwards. Trail runners might withstand the water better, but have less ankle support. In the town just outside the park, you can rent water boots if you want to go that route. One short spot was chest deep in water, others found a ledge to hang on around the pool. Call the park service and ask about all of this.
As for those who might not be up to the 16 miles, they should just hike up from the bottom and meet you. That way, they could go as far as they felt comfortable. I think the hike took 10 - 11 hours for us.
It is a fantastic and memorable hike. Would love to see pictures from it if you go.