SS Royal Oak - Smudges on midcase / lugs, help!

[Watchyourlanguage]

Hi, first time AP RO owner here.

I have mild OCD and stress over cleaning my watches every Sunday - a sort of meditative ritual if you will. However, cleaning my new RO is something else with its angles. There are some smudges that just won't come off and it's driving me nuts.

For longtime owners and experts, how the heck do you remove these stains on the midcase lugs??? Hope I haven't damaged the brushing rubbing it too much with a microfiber cloth. If there are any tips I would be grateful.