Thanks Saybian & Peachlovingman.
Note that I am not trying to speed up the decomposition of my pile, it is already proceeding at a good pace, and I turn it weekly to keep things moving along. In the past I did a "rapid composting" experiment in which I turned the pile every day. I had heard that if you have the right mixture and you turn it every day, it will turn to compost in 14 days. Indeed, after 14 days, 95% of the mixture had turned to compost. So when I am in a hurry I try to have a good mix and also turn it often, which is what I am doing with this pile. There are a lot of fungi in the pile already, many of which I think are picked up from the remnants of previous piles in the nooks & crannies of my bin. I have been composting in the same bin for 21 years so I would imagine I have picked up quite a menagerie of microbes & fungi. Indeed when I transplant a plant from one of my pots, the soil is full of mycelium.
Here are some photos of my bin, taken a while back:
My current pile is about 4 times this size, spilling over the sides and about 3.5 feet high.
I grow a lot of plants in pots, both from seedlings and dug from a friends property. I don't have a lot of topsoil in my yard, so when I transplant to a larger pot or into the ground, I use a lot of compost and just a little topsoil. I would like this compost to be full of "good things", thus my thought was to somehow inoculate my compost with MycoGrow. I could of course inoculate the plants with MycoGrow when I transplant them as peachlovingman suggests, but I think it would be easier to just inoculate the compost if that makes sense (which would also add life to my pile). But I'm starting to think that would just be a waste of MycoGrow...?
I have recently gotten in the habit of gathering a few handfuls of soil every time I am at some wild place in the neighborhood (or region) that has a lot of native plant diversity and has not been disturbed for decades. The thought being that I am bringing more microbes to my yard. I have been putting these in the corners of my compost bin, but maybe that is not the best idea?
As you can tell I have a lot to learn about microscopic soil life.