You paint an entertaining scene...
I've never used the pop-ups feature and just rely on email alerts so haven't experienced the issue with the links not working. I wonder whether there is some sort of delay between the emails being sent out and arriving at your devices - mine seem to ping in quickly after the tickets are released and I've been quite successful (although not for anything in this for popularity). I did set up an alert for the Taylor Hawkins Tribute gig and had been receiving regular emails with the tickets at varying price-points seemingly available when I clicked the link, so had hoped that you had been successful.
I like Twickets because of the non-profiteering angle and I don't know of any other platforms that don't fleece you but there might be some fan groups out there on social media.