Travel between them is not as hard as people seem to think, but you will have to have a hub or two and I doubt it'll be cheap.

I'd hub in Fiji for a bit and from there you will be able to reach Tuvalu (see it while its there), The Solomons, Samoa, Vanuatu, Tonga, Kiribati among others. From Kiribati you can get to Nauru and the Marshall Islands.

You could also hub in Brisbane or Auckland but flight times would be taxing.