So using a volume with a folder for consumption is supported. Basically add the volume (in my case extradisk) to the app. This would mount it to /media/extradisk then I created a folder called consume/ in that disk and you have to give it read/write permissions for all users (so chmod it). After this adjust the corresponding env var in the paperless.conf in /app/data. In my case PAPERLESS_CONSUMPTION_DIR=/media/extradisk/consume then restart the app.
Also note the volume in Cloudron has to be read/write mounted! If paperless cannot write to it (for document deletion) it would simply not even attempt to consume documents.