You might consider what I do with really difficult-to-kill weeds and seeds.
I soak them for a few weeks in bins stuffed with the waste and then filled with water. They drown, and then rot quickly enough. It's a stinky process, and you'll probably get rat-tail grubs which are harmless even though they look creepy, but the end result is a nice liquid manure for the garden, and mucky waste at the bottom that can go onto the compost heap, especially if it needs a little moistening.
The only thing to check is that any resilient seeds have in fact been in sufficiently long that they do drown and rot. It's a bit gross overall, but it works, and the result is 100% recycling of your organic waste.
Between chipping or burning thick wood waste, drowning recalcitrant weeds and seeds, and composting more benign matter, one should never have to export any vegetation from one's property. And really, if one does so, in the end one is shifting nutrients from there to somewhere else...
...blow that for a joke!