However, the fix is really simple. Since all we need in an anchor date of a monday, write this case statement.
--===== Test the new formula ============================================================
DECLARE @Bitbucket INT;
SELECT @Bitbucket = CASE
WHEN Date < '19000101' THEN DATEPART(dy,DATEDIFF(dd,'17530101',Date)/7*7+3)+6
ELSE DATEPART(dy,DATEDIFF(dd,'19000101',Date)/7*7+3)+6
end / 7
FROM #TestTable;
GO 5
N 56°04'39.16"
E 12°55'05.25"