Internally, Access is doing just what Allen Browne's ConcatRelated function does. Fortunately, Allen's code will handle multi-valued fields so you can just use it in a query like this
INSERT INTO MainTable ( MealType, Meats )
SELECT MealType, ConcatRelated("Meats","TempTable","TempID=" & [TempID]) AS Expr1
FROM TempTable;
where [MainTable].[Meats] is Text(255)
and [TempTable].[Meats] is a multi-valued Lookup
field.