Here is the full story:
1.
There is the option to select or32 (i.e. OpenRisc from opencores.org) in my C::B distribution which is the "normal" 10.05.
So, no need to patch C::B.
(Apparently, or32 has found it's way into the official C::B sources...)
2.
I was a bit too enthusiastic when posting that I solved the issue. Actually, selecting or32 was just a first step in the right direction...
It turned out the C::B was confused by "R0", "R8" etc in front of the register value columns. Moreover, mips-gdb puts out a space at the end of the register value row, which seems to be another cause for a mismatch in the displayed register values (e.g. R1 gets the value of R0 and so on)
I tried (just a quick hack) to patch the code for the debugger DLL of C::B. This failed because C::B wasn't able to load my newly created DLL (didn't dig into details here).
Finally, I decided to patch the gdb source for MIPS.
And now it works with the or32 selection in C::B AND the patched mips-gdb.
Perhaps not the most elegant solution - but it works ;-)