Happy to share, with the starting caveat that the "best" way to hit all of these without having a few weeks to set up separate stops (plus Kwajalein, which I'll miss and am consoling myself by saying you're not allowed to take photos of anyway as the airport is on a US army base) would have been to fly Nauru Airlines from Brisbane --> Majuro rather than all the way to Pohnpei, spend two nights in Majuro, and then take the United Hopper straight through to Guam.
To enter the Marshall Islands, however, you need both measles and the most recent "bivalent" Covid jab. I was vaccinated for measles as a child but was overseas and have no record of it, and while I've had three Covid jabs, not the latest. I wasn't keen on two more jabs I don't need right now.
So instead, I did it this way:
Sat: Qantas, SYD - BNE; overnight there (booked with QF points, cash fares in Dec are nuts)
Sun: Nauru Airlines, Brisbane --> Nauru --> Tarawa, Kiribati --> Majuro, Marshall Islands --> Pohnpei, Micronesia (737-7 in their new livery) (I paid $1,087 AUD via their website, including the ~$200 promo discount. I was able to select a seat I was happy with when I booked, though it can't be changed online. Seat map the entire way was very empty.) Overnight in Pohnpei and explore there the next morning.
Mon: United, Pohnpei --> Kosrae, Micronesia (738) (8,000 United miles, and I note it's a slight backtrack, but I've read Kosrae is especially beautiful to fly into and I couldn't stomach missing it if I'm finally going to do this. This flight will also position me in Kosrae to catch the usual United Hopper the rest of the way to Guam the next day). Overnight in Kosrae and can explore there the evening and next morning.
Tue: United, Kosrae --> Pohnpei --> Chuuk, Micronesia --> Guam, US (738) (17,500 United miles including the following morning's sectors to Seoul, which is exceptionally good value given cash fares. Like with Nauru Airlines, I had to choose a seat for the entire routing and not by sector. Conveniently, from what I've read about the full United Hopper, the "better" side of the plane to sit on switches midway at Kosrae anyway, so I was fine choosing the one seat the whole way. This flight -- or at least when all three sectors are being presented on one seat map -- is looking pretty full, especially on the "preferred" side.) Overnight in Guam and explore a bit.
Wed: United, Guam --> Osaka, Japan (738) --> [Asiana] Seoul, South Korea (A321) --> [Korean] Sydney (773) (As noted, to Seoul is covered by previous ticket which originated in Kosrae. Still can't get over the value of just 25,500 United miles for all of that. I then paid $1,400 ICN-SYD on Korean. I was delighted to see a Delta award for 40,000 points on that flight as I have 41,000, but multiple errors and a call to a Delta rep who definitely knew what she was doing confirmed it was phantom space, so I had to dig the wallet back out. Jetstar also had a direct flight as well but it was $1,000 for the starter fare and left Seoul several hours later, so I went with KE as I've always been impressed by their Y class on the 777 --- 33-34 in pitch and maintained the original 3-3-3. I'd have loved a night in Japan or Korea but need to be home for Christmas as family is coming.)
And that'll do it!