Thanks for your advice, everyone.
Well, I bit the bullet and emailed Canon's Swedish service partner, and they told me they'd want 700kr (£70, $110) to even look at it, at which point they'd tell me how much to would be to fix it, if it needed fixing at all.
Since I'm not 100% there's a problem, instead I bought FoCal, an excellent lens tuning and measuring application. First, I tuned the AFMA (which was a little bit out), then ran some sharpness tests vs. my new 40mm f/2.8 STM.
Attached are the results. As you can see, at 65mm or so my 24-105L is sharper than the 40mm, but at 24 and 105mm it's considerably worse, with 65mm being over twice as sharp as at both ends.
Now I know this, I'm less sure there's a problem. Now I know where the softest parts of the lens are I can avoid them. Still, I'm curious if such a large difference is normal.