Thanks for the clarification @sdurrant. While I investigate whether this is something Looker has control over, I've got another idea for a workaround.
In the script here, I notice the
lookerIframe.style.height is being set to
data.height (as long as it's greater than 800). What if, instead of relying on data.height to be correct, the script instead checked for the height of the iframe on the page? That way, the page:properties:changed event can still be useful as a way to say when the height changes, but then you can be sure that the height is right regardless of browser.