@iamtyce@DougA I finally managed to solve the problem with an HDMI splitter and an HDMI-to-VGA converter. 😄 The latter doesn't change the resolution, but my projector accepts the analog signal in contrast to the digital HDMI signal, which it refused as "unsupported". I just had to adjust the picture a bit via the projector's controls, as it was slightly off to the left and only partly visible.
A mentionable obstacle was that only one out of three HDMI splitters I tried worked with the 1600x1200 pixels DMT signal from the Pi. The other two only accepted CEA signals (see HDMI mode options in the official Raspberry Pi documentation). Strangely enough, all three splitters look exactly the same from outside apart from the brand logo.
Well. Here i am again. Was playing the whole evening and the soundproblems have started again. Its like a degradation over time or something. I know it was perfectly fine after reinstalling the image, was testing it for quite some time out.
What can be the reason for such a weird problem? Like gimme anything you have. Far-fatched or not i dont mind.