To reply to a few statements/questions:
The inventory of coin varies from bank to bank. Some banks may have a few thousand dollars worth of halves while others may have $50,000 or more. Sometimes, a bank may ship the excess out but that costs a fee. Many times, banks will "trade" or transfer amongst themselves in order to meet demand. Think about the supply variables: location (city, rural or suburb), number of banks that have accounts at each armored car company, the number of armored car companies per city, region. There are probably a great deal of halves held in inventory, since they are the least used coin besides IKES. I did not get an exact $ amount, but my contact said they had a 'ton' in inventory.
As far as money laundering and govt reporting - while the $4k per week is a pattern, the bank knows how the funds are being used - they are being converted into half dollars. The source of the funds or where the funds are going are the two biggest concerns for the bank. The govt only knows what the bank reports to it. The opinion of the bank is that 'the less reported to the govt the better off they are.' The Patriot Act requires cash transactions totaling greater than $10,000 on any one business day to be reported through a CTR.
As far as ordering halves, all you need to do is ask the teller. It all depends on the teller - I've been in banks where the teller orders a few times and then gives you some excuse why they can't order anymore. Then I have gone to another branch of the same bank a few miles away and have had no problems with repeat orders. In my opinion, as long as you are nice and maybe bring an occasional treat, you should have no problems ordering what you want.
I hope this info helps.