NavList:

Frank Reed you wrote "I don't know if that's a church or maybe a Wake Island "Christians' Club", or (less likely, I think) it may be a misplaced photo. The latitude is consistent, and the image was listed by the photographer as "Wake Island". In addition, there's a substantial antenna structure visible in the original photo either attached to that building or behind it, which is consistent with facilities on Wake."

Wake was one of my earliest possible solutions.  I flew round and round it on Google Maps but could find no match.  I also read Wake's history.  I flew up an down the longitudes 160-170E and 160-170W and still couldn't find it.  The nearest photomatch I got was somewhere in Papua New Guinea, but no aerial.  

What you say about airfield constructors is true.  With all their plant and materials, they could probably build somewhere like that in their spare time without going over budget. I seem to remember reading something on Kindle about squash courts in Vietnam. DaveP