Interesting.
If you have a shared docked view, you could add two custom properties for current title and desired title. Bind the current title to page.props.title. Add change scripts to both that check for matching strings. Copy from desired to current when not equal.
Everywhere that you are currently setting page.props.title, send a message to the docked view to change view.custom.desiredTitle instead.
FWIW, this behavior could be leveraged to make a reliable refresh event detector, which is highly desired by some users.