Update: repeat visit from another tech today because even with the fixed shock dampeners, it still made more noise than it should (albeit less now); after a lengthy investigation of a really-not-maintenance-friendly machine (welded front panel...) it turned out that one of the front concrete counterweights had shaken loose.
This was very annoying to figure out, because, well, the front panel was welded - they ended up asking in the repair tech group chat whether anyone had any ideas, and someone came up with the idea of concrete block tightening, and shared that on these machines you can remove the rubber seal and tilt back the machine, and then stick a hand inbetween panel and drum to get at the front blocks.
Took them a bit over an hour to diagnose, repair, and run a test cycle to confirm. Total cost was... 0 EUR, because it apparently fell under the warranty for their previous repair, being the same issue within the limit of 2 months. Awesome.
One really cool thing that they told me, was that apparently "repair over replacement" is their standard policy; they do sell new machines, but only if they can't repair the old one within a reasonable cost.
I assume that's also why they have the trade-in policy where if you try a repair, and it ends up unfixable, they will apply the repair costs as a discount if you buy a new machine from them. As that makes repairs low-risk for the customer, and presumably helps them with customer retention at the same time.