Well, things are up and running again, but not the way it was.
Before 7.6.1:
My cable/modem was the DHCP server, AEBS was the bridge (connected with ethernet cable).
iPhone etc connected to AEBS. AEBS got the IP-addresses from the cable modem/router and passed them on. In that setup, I had 3 Airport Express connected wirelessly to AEBS. And a USB drive connected to AEBS.
After 7.6.1:
AEBS never managed to act properly as a bridge. Even with extensive support by Carlo TD (many thanks!). Devices could connect to AEBS, but internet connection was slow and would disconnect at random. We tried to set up the AEBS as the primary router of the network, but the cable modem/router wouldn't allow it.
I found out that I can get my cable company to reconfigure my cable modem/router to disable the router function, but that's an unsafe bet. I would lose the only wireless router in my home still working properly. Which means no internet and no forum support until AEBS is up and running as my primary router (yeah right 😉).
My final workaround solution:
All my wireless devices connect to my cable modem/router. Including all 3 Airport Expresses.
Airplay works again from my macs and iPhones.
AEBS is connected with ethernet cable, and I can access the USB drive connected to it.
No wireless job for my AEBS.
My conclusion:
7.6.1 breaks the bridge mode on the AEBS (at least with my cable modem/router).
I won't touch this setup again, until the next firmware update comes along and until I can spare another two days to clean up after the update.