Welcome to the forum. In my opinion, even with adding the best bacteria and having O2 for them to live you will only see a few inches of muck reduction per year. Search here for Diver Cody threads on how to build a suction dredge. Pump the muck to dewatering bags on shore, let the water flow out of them back into the quarry, the muck stays in the dewatering bags.
If you want the best bacteria that you can possibly get, I would call AquaFix
https://teamaquafix.com/ and discuss your problem and how to get a custom blend of bacteria. That will require you sending them a sample of the muck at the very least.
There is different bacteria that works in different temperatures, so what might be recommended for summer isn't the same blend that you use in winter. Talk to them and ask how much muck reduction you could see per year, and balance that against the costs of dredging over the length of time (and cost) that it would take to see a reduction in the amount of muck in the bottom of the BOW by using bacteria.
Please let us know what you find out - that information will be useful to other pond owners here.
