In the non RW world, we would simply trigger a recalculation when the tooltip / tab / lightbox etc opens and has a real size.
With stacks from different developers this is not always possible.
So, to a possible solution. It may well work by using Limelight instead of Popdrop. You can still launch Limelight from your Dossier button (just give it a CSS class of the limelight content unique ID that you set in the settings).
The crucial difference with Limelight is that it has a lazy preload setting. If you turn this on it may mean that the Pagelit calculates its size on page load as normal. This is by no means guaranteed as I don’t have that stack to try it but it will certainly be your best bet for a quick and easy first thing to try.