Even a few years ago I saw multiple projects based around donating your node to a collective for implicit distribution. IPFS nodes are easy to control and have multiple methods of connecting peers directly or via pubsub groups, publicly via the dht and privately via libp2p sockets.
You could easily build a Freenet style distribution system around IPFS and its pubsub system.
Publish a stream of hashes with low peercounts, have nodes subscribe to this and do some evaluation to determine if they should store it themselves. Most likely based around local metrics.
Or really you could do it however you wanted.
I have a feeling that people are going to fork the filecoin project for this purpose. It would give you everything you need to coordinate storing, and verifying that data is actually being stored and distributed, but you could remove the tokens/cost and have your own metrics around choosing nodes (instead of cheapest bidder).