I would probably try first with what I had to work with. To start with you may want to keep yourself positioned so that if necessary you can use your bucket to help push your way out if things get soft. Is there not a way to get material from somewhere besides in the creek to place in the stream to stop it? You might even be able to get a load of rock brought in and use the tractor to transport it to where it is needed. You could begin putting it into the area needed and work your way across to the other side. This would also help compact the new material. As others have warned, things happen quick around sand/water. I have been stuck only twice with my tractor and both times were in a stream bed trying to slope the sides. Good luck.
Do you mean I wouldn't want to use the gravel from the stream because it would increase the chances of getting stuck?