It seems that the NAT-implementation is simply broken for any setup but randomly selected default.
I went back to 4.0.5 VMPlayer, and for a while that seemed to work, but after 19 reboots the NAT stopped working, and the only way to fix it was to reset the virtual network-settings, where the arbitarily selected network works flawlessly, but any changes to that results in a failing NAT-setup.
This has now been tested on 3 separate Windows 7-machines (Professional as well as Enteprise) and they all have this same issue, so I doubt that the problem is on host-side.