FYI for anyone else seeing this: I was still getting these timeouts even after the authentication fix from Rohan, and for whatever reason they were breaking my (very simple) bash looping script to push updates to the device. I took a new tack and wrote a simple Node app to re-render and push updates, but only whenever the screen’s content has changed, and this seems to have fixed the issue for me (and is a lot nicer on the Tidbyt API as well).
You can see the details of that app in my post over in the Developers forum: Strategies for Self-Hosted Apps? - #5 by CyberMonk