I too......have always felt (since the birth was during Sukkot) that He was probably born in a sukkah and since the early translators were not too familiar with Hebrew terminology....they thought "food shelf" (all sukkahs have them) meant "manger". This would be more understandable to 16th century English readers than a sukkah "food shelf".
I especially liked why they just didn't stay with Elizabeth since they lived relatively close.