Qatar's love of married segments is causing me grief.

I'm trying to book DME-DOH-JFK as part of a DONE4, departing DME on the (second) last departure (about 7pm), nine-odd hour layover in DOH and onto JFK. However, despite ample D availability on both flights, it's only possible to book the earlier DME-DOH departure, making for a greater than 12 hour layover.

Is there anyway around it?

Would it be possible to book the last DME-JFK departure, create a stopover in DOH, then book DOH-JFK , and then after booking, attempt to move the DOH-JFK to one day earlier? I suspect the system will reject it but I thought if I made the change 'from the back end' (by moving the DOH-JFK flight rather than the DME-DOH flight) I might have a chance.