P Lyons wrote: Compost materials would require some sort of processing (cutting/shredding) or larger diameter pipe could be considered
You don't mention whether or not you have electricity? If you do, is there room to install a garbage disposal before the pipe goes outside? It would definitely process your compostable materials down to a small size that would break down quickly. If you don't have electricity, you could use a hand-crank food/meat grinder to do the same job.