In case you're following this story, Recyclops confirmed that they do in fact store recycling in a storage unit until there is enough to transport to the recycling facility in northern Virginia, and so it was likely a misunderstanding that my recycling ended up in an empty unit.
In the end, I did decide to cancel my service for a few reasons:
1) When I talked to the storage facility owner who found my recycling in his empty unit, he had no idea Recyclops was storing their recycling there. He was pretty upset when he found out because it is against their policy for people to store trash or recycling in their units.
2) We never did get any bags, and I really don't want someone coming onto my porch and breaking down boxes, etc. We don't always want everything on the porch recycled, and it's also kind of a strange and jarring experience.
3) They just seem generally disorganized. They consistently took several days to get back to me when I sent an inquiry, and when I gave them my feedback about why I was canceling, I didn't get the feeling they took any notes or were interested in passing it along, so I don't see things improving anytime soon.