Was due to fly: LIS-GVA (TP) - WAW (LO) // overnight // - PEK (LO). Ticket issued on LO ticket stock in biz.
Long story short: Less than a week before I was due to fly, GVA-WAW was canceled. LO offered rebooking only on the same routing, meaning I'd have to overnight in GVA and NOT in WAW (which I would have preferred).
If there was no overnight in WAW, I would have preferred to fly LIS-WAW-PEK (TP, LO), though the LO codeshare had no biz availability. They refused to entertain this, even if I was ok to downgrade to Y on the first segment.

After going back and forth with them, I got nowhere. I decided to accept it and would try to get compensation for a forced overnight in GVA under 261/2004 (I would have had a place to stay in WAW).

About an hour before I was due to leave for the airport in LIS, I get a call from LO telling me they're overbooked/a J seat is INOP on WAW-PEK and if I would be willing to switch. They ended up booking me the day after (so no overnight), LIS-FRA-PEK (TP, CA)....

I don't quite understand the lack of flexibility in the first instance, but was happy to accept the rebooking + promised comp in the second instance.

What could have I done differently in the first instance to get rebooked?

EDIT: I've read the rules above. It seems the first instance was SKCHG, the second was IRROP.

It sucks that they're so inflexible for SKCHG.