So the 27 hour time probably makes it impossible anyway, but the other problem is QR's system already knows about all the flights.

I've been able to do something similar. My tickets were A-B / B-C / C-B-D. Initially I planned to check my bag for A-B-C, but I was able to get it tagged for A-B-D by simply not telling the agent that I was going to C and back.

The transit time at B for A-B-D was under 24 hours. B-D was a different airline to A-B so maybe the first airline didn't notice that I was actually starting at C. My bag travelled as expected.