Realistically, you shouldn't have to, and shouldn't want to.
Background: a scheduler-based model for evaluating effectiveness
Even if there was a way to do this (and there probably is - squeaky wheel gets the grease and all), squeaky-wheel-driven-development is something of a race to the bottom, pitting folks against each other over limited resources and ultimately rewarding those who both make the most noise and care the least about collateral damage.
Ultimately, this is akin to a scheduling problem: while there are numerous developers and designers working at SO, their time is managed by a handful of people based on a fixed set of priorities, which effectively limits what can be considered and the granularity with which time can be allocated. IOW, it's not enough to convince someone that a task is "important" - you effectively need to convince someone that it is more important than one of a handful of big chunky strategic projects. Which is why so many past examples of this strategy have involved massive Twitter polemics and the like...
What we're seeing now is actually an improvement over how it worked for years, when the algorithm was effectively "all resources go toward whatever project needs to be done tomorrow" and everything else was left to fight over resources that didn't officially exist. Meaning, stuff like bug fixes for Autocard effectively depended on a MTG fan on the dev team getting bored, and there was no way to report a meaningful status!
That said, it's clear from the data that the current scheduler is still very naive and unfair - and of course, this jibes with the sort of gut reaction we see in ourselves and others in response. Just as with early '90s operating systems (and, uh, 2010's Android) that seemed slow and unresponsive in spite of theoretically solid algorithms driving scheduling, the current process used at SO is at best a stop-gap until time can be devoted to something that actually works.
So to get back to your question: what's most needed here isn't pushing on individual tasks, it's more feedback on the perceived experience for all of them. Everything from little annoying bugs to big chunky world-breaking problems. Encourage folks to speak up, everywhere, every time - politely, but stridently. Give feedback on the roadmaps, point out when little things are overlooked and big things are just... not done.
Be the equivalent for SO of us grouchy Android users who finally motivated Google to stop screwing around with excuses after a decade+ and produce a usable phone.
And most of all... Don't get bogged down in minutia. There are literally thousands of things that should be being worked on here right now - and folks at SO whose job it is to make sure that they are. Don't try to do that job for them, just make sure they don't forget that they still need to do it!