That is a very nice little pond! I understand why you would like to keep it well maintained.
Since it drains to a creek, I assume you can pump it dry? How is the pond sealed? (Clay or plastic liner?)
If it does NOT have a plastic liner, I would pump it dry prior to your most likely hot and dry weather. (Middle of July to late August?) Let it dry as much as possible. (It might be stinky during this period.) If it rains, then pump it dry again.
I would then rent the largest mini-excavator that I had the capability to haul. The rental place will also have an equipment trailer for rent. Have them install the widest bucket they carry for that machine.
The rubber tracks will not cause any damage driving over your rocked shoreline. You should be able to move the muck out of that pond in a day. That type of machine is very easy to learn, and you will be pretty efficient in 30 minutes. IMO, you can only make two operating errors. First, driving sideways on a steep slope and tipping the excavator. Second, digging too deep and excavating through the clay liner. You can also make a "management" error, which is to dig into a utility or pipeline. Make sure you call your local service 3 days before you start any excavations!
With a fairly large mini-excavator, you can scoop and swing out a bucket of muck to your spoils pile over most of the pond. In the deepest part, you may have to move the material twice to get it beyond the boundaries of the pond.
The more difficult part is handling the spoils. If they are still very runny after your pond drying period, then you will probably have to pound in a section of silt fencing and dump over the fence. If they are as firm as pudding or even stiffer, you can probably pile them on the bank.
Even better, would be to dump the bucket into your conveyance for removing the spoils. A dump trailer, buddy's pick up, bed of ATV, rented concrete buggy, etc.
If you can't move it then, there is a little "dozer blade" on the front of the excavator. You can spread the spoils with the blade and let them dry, and then move them to their final destination in small bites if needed.
You have eyeballs on the actual site, so I am sure you can improve on my suggestions above. In my area, I could rent that equipment for less than $500 and do it over a weekend. That gives you more time to work, and no extra fees until you go over 8 hours on the meter.
Way below 10K, but lots of labor on your part - although it is fun to operate even a mini-excavator in small doses. It will not be as clean as a big contractor's ability, but you would still get your main goal accomplished.
Good luck on your improvement project!
