I usually handle large data moves in batches by setting up a loop and copying a set amount. Since these are during production I put in a delay to prevent hogging all the cpu. I don't know if this is practical for your situation.

InsertMore:

WAITFOR DELAY '00:00:05' -- 5 second delay allow other process some CPU

INSERT top (100000) INTO NewTable

SELECT columns

FROM OldTable

where id between @ID_First and @ID_Last

and ID not in (select ID from NewTable) -- Not already inserted

if @@rowcount > 0 goto InsertMore