Microbes are present in your pond enviornment, but there MAY be some faster acting types in their "black art" mixture. I can tell you without hesitation, you are NOT going to make a dent in the sludge in 6 weeks. Native or added bacteria will need the aeration you now have to work efficiently. Microbes work, but not nearly as well as they are claimed to and yes, most of the bacteria that work best on detritus digestion in your area are already naturally present.
Take some measurements of your muck depth to determine if aeration alone is helping to reduce it. Muck or sludge than can be removed with bacteria comes from hevy loads of leaf or other organic debris entering the pond from runoff or such as leaves falling from the trees. If you have little leaf litter, grass, or other such organics entering your pond it is unlikely bacteria or "microbes" will have any effect whatsoever and the "sludge is likely just soil.
Before you drop a ton of money on a "maybe" cure, find out if your sludge problem is from decaying matter or from soil erosion. read, get it tested. If it is mostly soil in comosition, manual removal is the only option. If it is mainly detritus, you could heavily stock tilapia for LOT less money than the microbes, get better, faster results in muck reduction, eliminate the FA and provide several tons of natural fish food to your predators in the late fall. Todd Overton or other PB members in your area could get you the tilapia and offer excellent guidance with an onsite consult.
