What about spoofing IP addresses (bittorrent DHT / IPFS / etc.) or a similar technique, so that the police think illegal material was shared from that IP, and when they come to investigate they find large quantities of random data, which they think is encrypted?

Modern PCs are as secure as a loaf of bread in a mob of seagulls.

Use malware to actually install sharing software and hide it from the user and at the router. Then use actual full-disk encryption software and make a real hidden partition and dump the bait files from the file sharing into it and leave the forensic traces. Then wipe the malware and delete the password and the FDE is unopenable but the courts will never believe the user.