Good news Update
I have been re-clicking the live chat all day today, probably many hundreds of times (no exaggeration), I got through once with a 20m wait, but then I switched to my email app to get the booking reference, and when I switched back, it said disconnected (on man amateur hour), and I could not reconnect no matter what I did. That was around 4pm local time. After this I also disabled battery saving just in case.
Fast forward to now, almost 9pm, and a few hundred attempts later, I again get connected with a 17 minute wait, which shortly after jumps to 40 minutes, but then at about 28 minutes wait it actually connects.
I explain my situation, and then another long wait while the agent checks my booking (about 15m), then the agent proposed a SQ business class flight on the same day which was great, but then as I said that's fine, I think it must have become unavailable because the agent said, they can no longer book it, what about a day earlier, to which I said no since I already had accommodation and plans. Agent then offered CX flight a day later (than original) and again business, so that was good.
Overall, once I could talk to the agent, it was fine and no issue, they did not try to book me in economy or anything, but just getting to actually speak to the agent was mission impossible and took me many days.
If you do manage to make the queue, don't do anything, don't touch anything, just keep that window open and don't let your phone/laptop lock, even getting to this point is akin to winning a lottery.