Airline financing is quite complex, since airlines are highly leveraged operations. Not only must they purchase (or lease) new airliner bodies and engines regularly, they must make major long-term fleet decisions with the goal of meeting the demands of their markets while producing a fleet that is relatively economical to operate and maintain; comparably Southwest Airlines and their reliance on a single airplane type (the Boeing 737 and derivatives), with the now defunct Eastern Air Lines which operated 17 different aircraft types, each with varying pilot, engine, maintenance, and support needs.
To sum up: a lot depends on your own stamina because island hopping means packing and unpacking, getting on and off buses and ferries. Limit your choice of islands to perhaps one or two less than you think you can manage. Maximise transport links to avoid backtracking or port-transferring and since you are traveling high season be aware that you will usually need bookings ahead at most places. It is possible to turn up on an island and not find a place to stay or have to make do with a third-rate option.
Since airline reservation requests are often made by city-pair (such as "show me flights from Chicago to Düsseldorf"), an airline that can codeshare with another airline for a variety of routes might be able to be listed as indeed offering a Chicago–Düsseldorf flight. The passenger is advised however, that airline no. 1 operates the flight from say Chicago to Amsterdam, and airline no. 2 operates the continuing flight (on a different airplane, sometimes from another terminal) to Düsseldorf. Thus the primary rationale for code sharing is to expand one's service offerings in city-pair terms to increase sales.