Finally after some days accepting status quo I found some time to thoroughly examine that thing again. Last time I was stuck at the point of updating the network driver by uninstalling the old one first, forced so by the Intel-Network-Software (which, guess what, didn't work in my case remotely
) - however I did revisit the fact that updating Rapid-Store-Software did the trick at least till reboot.
Now next step, as this software is pretty much not so useful (ain't it?), on an ordinary Workstation I tried uninstalling and this finally resolves the issue on all workstations in question so far.
Also my impression is, as other issues are already addressed with hotfixes this particular one, should one be hit by it, will not be recolved too soon as it maybe is too seldom and there is some probability that this is simply the shitty intel drivers or whatever? I got no definite response in this tickets and I don't know but now it's also not important anymore.
Also: it seems the RST-Software only interferes with Avast if a 32bit RST-Software is installed on a 64bit system.
Regards