leeinmemphis,
The decision on DIY vs "outsourcing" depends on a lot of variables including time, money, and equipment. This time of year is generally wet and heading towards really wet conditions. If you are in a hurry, then outsourcing is probably the best choice.
You have a lot of material to move. With low sun angles and wet conditions for the next few months, that material will not dry out sufficiently for you to remove it with your D4. Late next summer will be the earliest time you can move it with your dozer, IMO.
A track-hoe offers an efficient timely solution. I'm not familiar with the size of your hoe and the reach and that would be a determining factor in your decision. Assuming it is suitable for the work, knocking out a hole in the dam and then removing the material is probably the best approach. Pumping is an option, but with your equipment, it would be very easy to just take out a small slice in the dam and when finished repair it with good well packed clay.
A couple of other options include, as DD mentioned, raising the dam and/or creating an in-place island of muck ringed with clay to hold it in place. I've created such islands in two ponds that I have renovated, but didn't have the 5 feet of muck you mention. That is a lot of material.
Regardless of your choice, I think I would use this time to also remove the trees that appear to be on the dam. They add to the accumulation of muck and also add risk to the integrity of your dam. Good luck!
