Well, today the US government released records from the 1940 census to the public domain, giving us a whole new body of material to work with.
So to kick off this new area of exploration, let me present for the first time the listing for Beth Sarim as it was polled on 4/18/1940:
Here we find that Clayton W. Short and Frances B. Short were the caretakers of 4440 Braeburn Road, San Diego, California. This shows that by 1940, the Balkos had already moved away from Beth Sarim, replaced by the Shorts from New York City. Helpfully, the census asks where the individuals in question lived on 4/1/1935, where we see that the Shorts had earlier lived in NYC. This suggests that the Shorts were Bethelites relocated to Beth Sarim to replace the Balkos. Unknown of course is why the Balkos were replaced. Did they leave Beth Sarim of their own accord or were they fired? And if the Shorts were still living in 1935 in New York City, then unless there were other caretakers residing at Beth Sarim in between, it seems like the Balkos were probably not replaced until sometime after April 1935.
I just examined the 1930 census and I see that at Bethel in 1930 there lived a William C. Short, lodger, who was 31 years old and born in Utah. This matches the Clayton W. Short above who was 41 in 1940 and also born in Utah.