I would just keep turning it..
Then what ever is drawing the flies, gets into the other stuff inside and does a couple of things, it incorporates it into the compost inside, hiding it away abit from the flies by covering it.. and then starts the composting process for it, as it gets next to other compost that's been started/innoculated and get's it going..
Remember you really do need more browns..
Picture your compost pile like a camp fire..
You get alot of wood, and just sprinkle on a wee~bit of the started fluid or gas..
And it goes..
but not mixing and incorporating the old wood into the cherry red wood, won't get the new wood started...
Does that make sorta sense or a picture for you..
The compost needs to be turned into it, say every week....
The composter is in a shady spot in my backyard. It is under a tree and has a pretty good lid so I'm not sure how wet the inside got during the rains
When it's shadey, and say the ground is wet from rain, *which soaks in at somewher'es/somepoint if it's alot of rain~which in turn keeps the bottom of your pile wet...
Doesn't really hurt it, but does make it go "stagnet" as a word I will use.. it slows down because no air can get to the bottom... if you turn a number of times, it keeps it moving and a wee~bit of aeration into it...
*I know how that goes, for my bins and on wet season's composting can be challenging..*
What does your compost look like right now??
Dark, rich, crumbly..
Or big hunky pieces you can still tell what it is?
*When did you say you actually started the pile?*
And are you able to leave this one alone and start another one to let this one rest and finish composting??????