Just made three attempts at rebooking the 03APR BKK-BRU booking on OAL.

Agent 1: yes of course, I will do that for you, providing there is availability. Couldn't find it on TK or CX. Then the line got disconnected.
Agent 2: no, only possible 72hr before your flight.
Agent 3: no, only possible 72hr before your flight.

So it seems they are only rebooking on other arilines within 72hrs of your cancelled flight. Just sucks that the first agent was about to do it anyway when the line got disconnected
Flights will probably be fully booked 3 days before on this busy route.