I — Sun & palm
Your reference, reduced: one sun low over one wave, one palm, nothing else.
Identity
Logo directions
Modernised from your reference
The sun-and-palm idea, drawn with far fewer lines so it reads at any size and holds up in one colour.
J — Two horizons
Two level lines at different heights — the winter sea and the summer sea — with one sun between them.
K — Wave & frond
A single wave on one side, a single frond on the other, drawn as few times as possible.
L — Solstice
The same sun twice: high in one half, low in the other. The two seasons in one mark.
M — Three lines
Your mark above the name set in three lines, the way your reference holds it.
The direction you liked
Thin single-line geometry, one terracotta point, the name in classic capitals — five ways to draw it.
A — Two halves
A circle split in two, one point for each island, above the name in classic capitals.
E — Horizon
The same circle opened by a level line — a sun sitting low over the water.
F — Two islands
Two thin circles touching, a single terracotta point where they meet.
G — Meridian
The split moved off centre, so the two halves are unequal — two seasons of different length.
H — Sea line
A wave drawn through the circle, the sun held above it.
Other directions
Kept for comparison, so you can see what you are not choosing.
B — Monogram
Interlaced D and S inside a double oval, with the name in flowing italics. Couture feel.
C — Horizon sun
A sun setting over a gentle wave, with the name in fine, airy lettering.
D — Editorial
Pure lettering stacked like a magazine masthead, with a single terracotta dot.