I would probably get some more compost and pick out the junk. We used to get "penitentiary" compost which was full of plastic bits. They disappear after a while...... OTOH we also get free aged cow manure which is full of weeds. The trick there is to put it in a veggie garden where you plant in rows and can run a hoe along it to pull out the baby weeds, or else to cover it with black plastic mulch - at least, that was my experience. Putting the aged manure in my asparagus garden with wood mulch on top was a disaster because the mulch did nothing to stop the vigorous weeds.

I'm debating on buying a leaf shredder. I have tons of oak leaves but I can't get them to compost worth a darn. Most shredders are either really expensive or poorly rated though. So frustrating lack of quality manufacturing anymore.

You can rake or spread the leaves on your lawn and then make a couple of passes wit your mower to chop them up. Does mean you have to rake up the results however :-)

The alternative is to fill garbage can about half full and use a string trimmer do the chopping/shredding work.

Ooooh, I am game to try the string trimmer trick! Tried the running over with the lawn mower, wasn't very efficient/effective at least with our mower, seemed better at scattering them than chopping efficiently. The electric leaf mulchers that they sell in the lawn and garden stores are kind of like glorified string trimmers anyway!

Edited to add that peat to purchase at Home Depot is the cheapest option I can find so far, and I know peat is not the greatest product for the environment. Am working on getting our compost set up. They are out of the hardware cloth I need for the sides so waiting for my order to arrive. We want to make it as mouse-proof as possible since we are already inundated with varmints here on the edge of the rural suburban interface. Once I get the compost set up, I can mix in manure as an accelerator or make manure tea, but that's not what I want for the immediate concern.

Update. We tried the string trimmer technique and did get some nice leaf mulch. On its own too big pieces for just dumping, but I used my rock sieve to sift out the small bits and they were marvelous. Used the other stuff left over for mulch around some trees. Very labor intensive though. Not a time effective solution. Will be good for using once we get the compost bin set up. Still waiting for fencing to come in on that project.

That's why I sieved. The percentage of the high carbon material was small. I got some peat moss for the rest. The bulk was topsoil so now that it is in there, every year hopefully can just amend with compost once we get our bins going. Have planned on doing the compost bays with metal stakes for the corners and 1/2 inch hardware fencing. They were out of the big rolls of fencing at our local stores so waiting and waiting for an online order to arrive. Meanwhile the shredded leaves are going to make great mulch for under our trees. I'm trying to create some wild woodland garden islands so less grass and less mowing. Having the leaves shredded keeps them from blowing away as mulch. We have gazillions, (well 30+) hardwood trees in our yard and I'm developing a "leaf management system." I inherited the property from my parents and Dad burned and burned as do many in our neighborhood. Ugh for all the smoke and ash. What a waste!

Perlite or vermicultie will add air space. Compost is an important ingredient but does not serve the same function.

That wood ash will give you potash that can be used in your garden, though sparingly. Lawns also appreciate it. Keep it away from acid loving plants, like blueberries.

We burn some but for us it's twigs in our campfire pit. We do save the ash and use sparingly. With a limestone bedrock acidity usually isn't a problem in soil here in the bottomland. I didn't think about buying straight perlite. Want all organic products.