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I only want to exchange torrents over my local network.
Is there a way for QBT to only communicate with peers on the local network?
Is there a way for QBT to make local peers a priority?

Don't use public trackers, DHT and make the torrents 'private'.

You can also use a ip blocklist in qBT which blocks everything but your local network ip ranges.
You won't need NOR want to port-forward qBT's listening port on your router either!

DHT, Resolve peers IPs/counties, exchange trackers, and a few other things should be disabled if attempting this.
You'll probably get much better results if you keep half open connections, global total connections, and per torrent connections very low -- like 2, 30, 8. You're probably not looking to connect to 100's of computers at once, remote or otherwise!

Thanks for the tip.  I currently just add the local IP address to the Peers tab.  It works, and works through my SOCKS connection.  The Peer feature seems clunky and not given much attention.  But I prefer using it for transfers rather than FTP.

The piece checksum validations done by pretty much all BT clients means the files are 100% identical.