A couple of observations and learnings from reading this site:
1. Beneficial bacteria are only helpful on getting started on the muck removal, you need to also provide oxygen for them to get and keep them working. It is a speed boost to the natural process of bacterial growth.
2. If you get your muck digesting quickly with O2, you will also need a means to remove the excess nutrients that will be created in your water column. If you have no means to do so, you are building up fertilizer in your water. The plants will use it for you. Think algae blooms and weed growth. You are doing the process of turning your muck into viable life again. Tilapia, water exchange, bottom draw, grass carp, are examples of managing this accumulating nutrient source, as in the case of fish, they will accumulate it in biomass. Remove that biomass to the dinner table.
3. Moving O2 with an aeration system is one of the most efficient ways to get O2 into a water column and move water, but you need a strong flow to work it down into the muck. If you have too much flow, you will have a boiling cauldron of fish and debris. With a more reasonably sized system, the O2 laden water will work into the top layer of muck, and over time may be one of the best ways as it will work on muck at a manageable rate. Best to start with aeration before the muck starts though as the process is slow. Plenty of threads here with more details.
4. Bottom draw system. It will pull O2 water down through the entire muck layer, and then dispose the nutrient rich water outside of the pond basin as the muck breaks down or is sucked through. The drawback is you need flow-through of water for it to work. No flow-through, no different than any other stagnant pond. Another advantage is any anaerobic bad stuff is put somewhere other than in your pond when it starts up, so no toxic compounds to skunk your fish. At least in your pond. Where it goes, you must be careful.
5. For a smaller pond, you can create an under-gravel filter system. A large version of what aquariums used to use. This allows an aeration system to pull water up through a pipe which is attached to a network of buried pipes full of holes under sand and gravel. Easy to build yourself but could be expensive. This system efficiently pulls O2 water down through the muck and gravel, and the gravel surface provides the surface to host beneficial bacteria that scrubs the water. It works like a bottom draw but can be run all the time. You could also combine it with a bottom draw siphon pipe for the best of both worlds when you have enough flow-through.
These systems need to run as frequently as possible to keep the aerobic bacteria alive that is working the muck. Let it stop for too long, and most of the good bacteria will die. Death rate likely depends on a huge variety of factors, but I have the same problem in aquarium filters if I lose power in my house for more than 12 hours. Rather than 8 hours and 16 hours off, create a schedule of 4 hours on, 8 hours off, or even finer time periods so the bacteria can "breathe".
I am trying the under-gravel filter in a larger garden pond, and so far, very happy with the results. It is keeping the water sparkling clear, making the goldfish easy targets for herons. So far, no algae problems despite flooding rain washing in topsoil.