Figured out a partial solution for future reference for anyone who comes accross this…
Before the popup appears, it tries to preload everything that’s visible in the popup, so that the popup appears fully formed. So the user has to wait a few seconds while the popup builds.
Solution was to hide any elements in the popup that are causing the delay, and in the workflow that opens the popup, to also have it make those elements visible. I had to add in a slight pause (.1 of a second worked) between the workflow step opening the popup and the step making the element(s) visible.
Now it works well – the popup opens immediately and during the “delay” of a few seconds the popup is rapidly filling with content, so it gives the impression of things happening, rather than a confusing pause. This is only for the first time the popup is shown – subsequent times it opens fully formed since it’s already been built.