Hey there! I'm really glad to hear that you're enjoying Tether! I certainly encourage you to publish any material of your own related to Tether, and I only ask that you include somewhere that the work is "inspired by the roleplaying game Tether by Adam Baffoni."
Also, I would love it if you could let me know if you do publish your writings so that I can share it on my social media pages! If it is a direct publication of your journal entries, I think that would be a fantastic resource for new players to see what a playthrough looks like. Thanks!