Note, I haven’t talked about this much at all, but it did work when I implemented it
Image shows the “Events to queue new jobs” section in the Options screen within WP2Static.
But, this requires you to be using the Jobs / scheduling functionality of WP2Static, which is a bit more complex than just clicking the button on the Run screen to generate your site.
If you really need dynamic pages, and don’t want to change them to a serverless function, then YMIR can be an interesting alternative. You don’t get the security benefits of a purely static site, but the performance benefits are theoretically great (not sure how much it costs).
I work at Strattic (not in support) and know that we do help some customers to get some dynamic filters working on their static sites, but we’d need to get more specific info from you to help advise about that (what plugins/themes these filters are coming from, along with any customisation you may have applied). Strattic support team has also received your enquiry, but may take a couple more days to get back to you, if not already.