Laura
Somewhere I think we have a report on the trees of Nikumaroro compiled by Josh Gillespie during the 2001 expedition. Might be on the website, and if not Tom King or Ric surely has it.
There are trees on Nikumaroro capable of being carved, particularly the coconut palms, Kanawa, Buka, and Ren trees. Most of the trees mentioned are fairly long lived as far as I can tell, so many of the existing mature trees were likely there at the time we're interested in.
In the Old colonial village, there are many palm trees that have foot holds cut into them so that the colonists could easily climb them for the nuts. Most of the foot holds end about 15 ft up, and the rest of the tree above that has none reflecting the growth since 1963 when the colony was abandoned.
We've looked for carvings on trees, but not found anything that we'd consider a likely candidate for AE or anyone else for that matter. I suppose there are some carved trees in the old village, but not legible to understand. I don't recall anything around the 7 site that looked like a carved tree. I do know that carvings on trees in general get pretty obscured over time as the bark tends to swell and overgrow the areas carved, so after 75 years, I doubt that any 1937 carving would be apparent or readable.
I hope that helps.
Andrew