Success! Thanks, Rankourabu.

For the record, where I think I went wrong is that I originally reserved and held the S. Asia - Australia segments (90,000 miles) and then called to add the flights to and from the Pacific islands, which should have actually dropped it down to 50,000 miles, because S. Asia to Oceania via Australia requires fewer miles than S. Asia-Australia. For whatever reason, it didn't work, and the Indian call center agents were unhelpful.

Following Rankourabu's advice, I reserved (actually accidentally booked!) a 50,000 mile business class open jaw itinerary Bangkok-Sydney (stopover)-Tonga returning Fiji-Auckland-Singapore-Bangkok.

Then I called in and changed Fiji to Apia (Apia not bookable online) and also changed Auckland-Singapore to Auckland-Perth-Bangkok. Fully changeable because it was less than 24 hours. Still 50,000 miles, and it even knocked $80 off the fees.

So as not to blow the agent's mind, I then hung up, called back, got a different agent, and added the Phnom Penh-Bangkok legs. Still 50,000 all in for the itinerary in the OP above, almost entirely in business class, just two short segments in economy.

I think I had Filipina agents on the last two calls, they were more helpful.

If availability opens up in business on the short flights I had to book in economy, can I bump up to business on those flights for free or does United charge for that?