Join or sponsor an Amateur Radio expedition.
Many Amateur Radio enthusiasts like to collect radio contacts and postcards confirming these contacts (called QSL cards) from rare and distant locations (called DX).
The richer hobbyists will sponsor or join a DX-pedition to some of the more exotic, uninhabited, locations that are rarely heard on the air. Inhabited places already have Amateur radio operators, as it is widely accepted as a hobby or public service. Often these DX-peditions are timed to coincide with specific, well known yearly contests where they compete at generating the most ham radio contacts or the highest contest score.
An argument that is often put forward when advocating for permits, etc. is that these expeditions (and the related contests) have value as emergency preparedness training exercises. Organizing an effort to take equipment, wire, antennas, portable or improvised towers, and portable power generators out into the middle of nowhere with no infrastructure and set up contact with the world can yield some insights into readiness and operations after a hurricane, earthquake, or other event in civilized areas when ordinary communications has been disrupted. Those participating in a contest from their comfy air-conditioned home may find special categories or extra points for using low power to make contacts or for disconnecting from commercial electricity and using non-polluting solar/natural power sources. The overlap with actual emergency ops isn't perfect, of course, but maybe it doesn't need to be.
As for these specific islands, I found previous efforts by Googling a location+" dxpedition"
Palmyra Atoll - K5P
Johnston Island - K3J
Notes military has been busy clearing land mines and chemical weapons....
Wake Atoll - K9W
Reading through these stories, when money is discussed you will find most of the financing comes from the groups themselves. Although it is possible that some hobbyists may include a few dollars with their request for a QSL card, and some of these efforts yield tens of thousands of contacts, not everyone wants a card. Also, most countries' Amateur Radio regulations prohibit soliciting for funds directly on the air.
I would imagine that enough resources, skills, money, and networking would yield a chance to be part of a group visiting one of these places.