Everyone is doing palladium missions at the moment because they pay well
This. It was never the highest-production commodity in the first place, but previously most people's money earning methods didn't significantly deplete it so the overall level stayed pretty stable.
Now people are buying it faster than it's being produced ... with the inevitable result that eventually it runs out everywhere, since a single mission can easily use the "normal" stock of two or three stations, and it takes weeks to fully recover.
Fortunately, there are plenty of options for obtaining it - some more effective than others - to suit almost any preference:
1) You have 24 hours for these missions, so scraping up crumbs from everywhere is possible. There are over 15,000 Extraction stations in the bubble, so you'll get there eventually and can maybe make a bit from basic trading with the rest of your hold along the way. (Looking for stations on EDDB not with a high supply but with an ancient 'last update' might be quite profitable)
2) Mining is almost certainly the most reliable. Even without mapping or visiting a RES - or much practice - a full wing should be able to mine about 400t/hour from a pristine metallic site, and get a bit of Platinum and Painite as a bonus.
3) In Extraction economies, some missions give Palladium as an optional cargo reward. Do those missions and you'll eventually have enough that you can complete it.
4) Palladium is a pretty common cargo type to find at the randomly-generated surface salvage sites, so get in your SRV and start collecting.
5) If stolen goods count (I can't remember) take a bunch of Palladium delivery missions from factions you don't care about, abandon them, and give the goods to this mission. The fines might add up to more than the mission reward, of course.
6) Are there some megaships/installations which can be robbed for Palladium? There are certainly some you could get other refined metals from. And Thargoid-damaged megaships the metals are legal salvage, too.
...
In other words, we have a dynamic economy generating missions which are well-paid but potentially quite tough to do, self-regulate on the "gold rush" side by automatically getting harder the more people do them, have multiple valid ways to complete them rather than a single railroad, and benefit strongly from wing cooperation and planning rather than G5-engineered brute force. It even ties into management of the BGS (Boom gives a 60% bonus to supply cap and regeneration rate) for some longer-term strategy.
Exactly what the forums have been asking Frontier to deliver, right?