During 2021, I have consistently been able to find business and first class tickets to from California to Asia on CX and JL. I booked four flights, then had to keep pushing them back further and further until I had to cancel all of them except one, which I moved to June. There were several earlier dates available, but I figured that Japan might finally be open by then.

I consider flights to Europe to be too cheap to use miles (my also-cancelled NYE trip to Lisbon cost me $378), so I have no idea about that.

The reality is that every time I book or change my flights to Asia, I have to spend an hour or two at the JL and AS Web sites to piece together flights that I can book. That does take time and effort, but if you are willing to do that, I'm sure that you will find something.