I agree that "Belyi method" sounds confusing. For example, calling it knxapp gives much better result in google.

Lilsirecho, according to your description of the problem - the boot itself works fine but the startup of programs got mixed up.

According to what I saw in KNOPPIX, the startup files living in /etc/rc?.d directories are hand crafted and when there's a new one got added by upgrade or installation of an application it results in great confusion. What I would recommend to do after the upgrade - remove all /etc/rc?.d directories and copy them again from the original copy of the KNOPPIX. This will probably prevent your new applications to be launched at the startup time (in case they require it) but at least it should bring you to the same state which the original KNOPPIX did. You can always start your new applications afterwards.

Hope it helps,
Igor