Crimson Castle wrote:

The compost is a closed black bin with a lid.

You need a bigger bin. A 1 metre cube usually improves the composting
far better than those plastic bins. The bigger mass can generate and
keep more heat to kill the seeds.

And I have the same problem with grass seeds from grass clippings.

Other things you can fiddle with are;
moisture level (you may need to add water)
bit of lime (especially if you put in gum leaves)
nitrogen (dynamic lifter is relatively cheap - add water).