So today I walked a bit through Shenzhen from the Louhu border station. (What a mixed experience!) I was first passing through Jianshe Hu and then through Shen Nan Da Dao towards KK100 and then a bit further. Every building I entered (except for one three-story book store) turned out to be a huge luxury shopping mall (such as MIXC, for example). I then turned into the quadrant south-east of the two roads. There I asked in a few convenience stores (e.g. 7-Elevens) and a few cellphone stores (some of them marked with big China Mobile banners). None seemed to offer the China Mobile 188元 plan that I originally wanted. At one cellphone store I was offered a SIM card from China Unicom.
Back at the station I finally decided on obtaining a China Unicom SIM card from what looked like their official store in the passage area. There was a line of Chinese clients ahead of me and one had to draw a ticket. The sales agent spoke English well, first inserted his own SIM card into my phone to confirm that it was indeed unlocked, and checked that the solution was working before he charged me. He took digital pictures of every client twice (once with SIM card in hand :-) and yes, he did also require ids (such as my passport; that might not have been necessary at the other earlier venue, who knows?)
So I now own a 100元 prepaid SIM card with a +86 number and will try it further inland during next week. I hope China Unicom's apparently a bit smaller coverage in comparison to China Mobile's will not become an issue there.