Herold,
It is possible that the TCP MSS adjustment works but note that it applies specifically to TCP traffic by modifying the contents of TCP SYN or SYN/ACK segments directly. It does not use ICMP to perform its work. For other kinds traffic (say, UDP or ICMP), the TCP MSS adjustment does not apply.
If you see the ICMP T3C4 messages being sent by your router, can you examine their contents using Wireshark and see what contents do they carry? Usually, they also hold the IP+L4 header of the packet they relate to. I would be interested to see if they still refer to some TCP traffic, or whether the related packet was a non-TCP datagram.
The Next Hop MTU of 1476 is correct for GRE tunnels (1500B - 20B for the new IP header - 4B for the GRE header).
Best regards,
Peter