Its a toss up between phone and online bookings, both of which are possible, but it can make a big difference to the taxes as booking the return online remains as 2 separate bookings with (generally) higher total taxes to/from USA and lower to/from the far east. If it is a really popular route you can even be pipped at the post trying to do it online by an agent, who has bagged the seats as soon as they appear, for a telephone customer. We lost our 'dream seats' between selecting and paying online on a weekend return from the Seychelles.
I've done it successfully via the USA number but that can close right at 01:00 UK time. As an anecdote, I once called the US from South Africa but the agent could not yet see the seats and eventually we gave up. The following morning I called UK, expecting them to have gone, to find they had somehow been reserved for me and we completed the booking and payment at that stage - I didn't know that was possible or permissible but I didn't complain!
Notwithstanding, I understand that the call centres are either on reduced manning or reduced hours at the moment so it might all be a bit more difficult under the current restrictions.
Best of luck - or maybe, hope it went well, if you meant 01:00 this morning!?