In regards to the post about an equal-area map for the Indo-Pacific region, why not use an obliqe local Aitoff-Hammer map?
Aitoff-Hammer is a projection for mapping the entire Earth, but it could also be used for any oblong-shaped smaller region, such as the Indo-Pacific region.
Aitoff-Hammer has a relatively symmetrical distortion-pattern. It's made by laterally expanding the Lambert Azimutha Equal Area projection.
An oblique Aitoff-Hammer would seem the most distortion-minimizing way to map the oblong-shaped region you spoke of.
Aitoff-Hammer is often just called "Hammer", and I'll so call it here henceforth, for brevity.
How Hammer is constructed:
Start with an oblique Lambert Azimuthal Equal Area projection. Say it's in equatorial aspect. Expand the map in the east-west dimension, by any factor, F, that you choose. In other words, multiply all east-west distances by F.
Now, re-label the meridians so that their labeling will be in keeping with the new east-west extent of the map. In other words, if F is 2, and you've doubled all of the east-west distances, then also double all of the longitude values of the meridians.
When Hammer is used as a world map, you start with a Lambert Azimuthal Equal Area map of half of the world, in equatorial aspect. The F value used is 2. That gives a 2:1 elliptical map of the world.
1. The map needn't be in equatorial aspect. Of course it could be centered on any place in the world, in any orientation.
2. The map needn't be a map of the whole world. The above-described process for making Hammer from Lambert Azimuthal Equa Area could be used for any size region as well. And, of course F needn't be 2. It could be whatever value fits the shape of the region you want to map.
I haven't heard of Hammer being used for mapping a region smaller than the entire Earth, but it could be so used, as described above.
Hammer was introduced in 1892, based on an idea introduced by Aitoff 3 years previous. (Aitoff applied the east-west expansion to the Azimuthal Equidistant Projection).