I don't really understand what the question is, or what should be the alternative.
The three islands cities will be able to pay for themselves with courthouses after the palace moved. At size 4 they will produce 9 gpt working 4 coastal tiles and have something like 6-8 maintenance with courthouses. So they are neutral or of benefit to our empire.
Before the palace move they are of immediate benefit, because they generate a trade route
If we don't get the palace to Osaka any city in this region will not be able to pay for itself for a long time. They need to build a courthouse first then they will need cottages to generate enough gold (outside of Osaka I don't see high commerce resources).
So I just don't see any alternative. If we go out to settle or capture near Osaka right away, we will not be able to keep more than 1-2 cities at one time and then have to develop them for a long time. While we do this our research is near zero.
One other small remark. You talk about mainland, like this would be the only landmass.
We only know Spain. I see no indication to assume that there are more AI civs on the island of Osaka.