Ah, now I clearly see the issue. The new firmware of the HC06 (version 3.0) requires AT and CR+LF instead of AT only, and there is no 1 second timeout anymore. So I should update the firmware of the CurrentRanger.
The new requirement of CR+LF was one reason why it got such a long time from me to find out why the HC06 is not responding to AT commands, and later on why it doesn't accept the AT+BAUDn command. After getting the version read (it was 3.0-20170609), some googling got me on the track. It appeared that the AT+BAUD9 command had to be replaced by AT+UART=230400,0,0 (& CR+LF) in order to get the baud rate changed.