You could try gently with a credit card wrapped in a tissue or similar, but the risk of scratching the veneer is real, and considering how great the condition is on these I think a less sharp, more purpose made implement would be better.
Cap replacement on a speaker this old is probably a good idea - the crossover is just first order I think so not at all intimidating to work on.
I am quite jealous TBH. Lovely speakers you have there.
It could be that you’re like me, and like a bit of bass. The HD600 doesn’t have much at all (fight me Senn fans) so you keep turning it up to get some impact until the upper midrange starts to hurt you.
Try a little bass shelf and see if your experience doesn’t improve.
(it won’t solve the soundstage issue with those headphones, however)