We once did something similar of the River Stort. Arrived late in the evening and extemporised a mooring; not realising how high the river was. What didn't help was that the local CRT bods opened the flood paddles that (Friday) evening and then buggered off for the weekend, so by the time we woke up the next morning the water level was a lot lower than usual and we were well and truly marooned. Several other boats were in the same state, but we all got together and freed the easiest NB, which then started snatching others. Being deep, and because we weren't on a regular mooring spot, Melaleuca was by far the most stuck; sitting pretty flat on the bottom with a good eight inches of normally wet hull showing all round. I was very sceptical that she'd ever move, but we used one NB roped to the front and another roped to the back and both took a good snatch at the same time and she came off very easily.
So what you need, Andrew, is not one, but two passing boats
MP.