I have some experience with this with my pond renovation in August 2015.
A cut was made in the dam, then I pumped the remaining water out to the top of the muck. The dozer began pushing from the edges, gradually mixing dry clay with the muck.
Eventually the dozer was able to cut down to solid clay near the middle of the pond, and make pass after pass, pushing the muck into a sump that a backhoe dug, then the backhoe with a big bucket was throwing it over the dam.
Some muck was left in the sump hole, covered over with about 3-4 feet of clay. It bubbled for about two years, but was a relatively small area.

If you are renovating, I recommend you get out as much muck as possible. We spread the muck out in a flat area just out of the pond watershed, to a depth of about 2-3 feet. It dried enough in a year for a small dozer to level it out. It's grassed over now, and I cannot even notice it is there.

My pond is only a quarter acre, so yours will obviously take longer than the three days mine took.

Make sure all disturbed areas are well compacted during the completion phase, especially the cut in the dam. I am still dealing with excessive seepage due to poor compaction and failure to take out all tree roots.