Flights between Port Moresby and Solomons

Hi there.
I'm living in Malaysia and planning a short trip in late May/ early June, which can't be any longer than Sat 28- Sun 5, to visit Port Moresby and I would like to also include a brief visit the Solomons.
The Air Niugini flight KL- POM (which seems to be the only logical option) runs only once a week on Saturdays and their POM-Honiara seems to operate twice a week but only Friday and Sunday, with returns Saturday and Monday, seemingly making it impossible to get to the Solomons just for a few days in the middle of the week. Does anyone know of other ways to do this, bearing in mind the limited time I have?
I did look at POM- Brisbane-POM on Air Nuigini with Brisbane-Honiara-Brisbane on Fly Solomons in between but the last part is also not daily and schedules don't really work.
Appreciate an advice from the knowledge people on this forum!

Pacific Blue fly Bne-Honiara return on Tuesdays and Thursdays, and Our Airline had one flight a week, meaning there is a bne Honiara and a Honiara Bne flight nearly every day. Solomon Airlines is Monday Wednesday and Friday, as well as Sunday over summer. All flights leave Brisbane in the morning and return in the afternoon, except Our Airline (not sure when they fly).