Well, luckily I had not sent the old modem-router back to the ISP yet. I plugged in the M2P-Pi and a PC by ethernet and started them up. I could access the M2P-Pi via its old address. Then, under WiFi/LAN – Fixed LAN-IP Setup, I unchecked „Set fixed LAN IP-Address“ and saved and shut down the M2P-Pi. Plugged it back into the new modem-router network and all was fine; the M2P-Pi took a new Fritz 178 address.
Would still like to know though if there is any way into the settings from within the M2P-Pi itself.