Whats the turn-around time on your bins?
I usually empty out bins about every 6 months as that suits me for using the compost at the points when most of the plot is either being cleared in autumn, or is empty prior to the spring planting season. A hot bin can work in half that if you get it right.
As the bins are stacked and start working, the contents sink rapidly, so it can take a few goes to get them full, but then you get a big load of compost back out. If anything isn’t rotted enough, I chuck it back in a bin I am filling for another go.
Regarding nasty weeds that Grubbypaws wants to compost. There are a few I don’t put in without prior treatment - buttercups, couch grass, bindweed and dandelions. Treatment consists of leaving them out in the sun to dry to a crisp, or soaking in water. Both take a few weeks and the water option makes for a stinky old brew, but the compost heaps seem to like it