Folks, I would like to provide a quick update:
- ended up flashing latest ASUS firmware
- I think I found what was causing the trouble: suspecting "Enable DoS Protection" - when it is off, no issues, when it is on, trouble starts.
IMHO there is a bug in that code which makes ANY ASUS based firmware not to get along with DSL modems. Same problem was on AC56U.
Now my DSL internet is gone for good (there were are other problems - with DSL itself), and I am keeping this setting off with the new modem...
A developer need to debug to confirm this issue - I am not in a position to do that...