Sorry for the delayed answer, but it took me some time to figure out the reason for this issue and it looks like that it was an incompatibility of Freespace with the new headset. When I bought and installed it Freespace and FSO was already imstalled. Your advice also didn't work, because Freespace simply ignored the setting of the headset being the standard output device. So I tried a reinstall of my old FS2 together with FSO and everything that comes with it without success.
So I tried something more risky and deinstalled everything again. Then I bought FS2 on gog.com, installed it again with FSO and see there it works now. I can't say for sure what the reason for my old FS2 version had not to recognize the proper standard output device and I'm sure this isn't the perfect solution, but it helped and I can play whenever I want now.
I also tried the wxlauncher instead of the Windows launcher and that also worked on my old installation, but that launcher is yet still too much in an alpha or beta phase and not really of any practical use for me, so I decided to abandon it and go the other way which was risky, but helpfull.
THX