Almost no bank gets boxes from the federal reserve, they all get them from cash logistics companies such as brinks or gardia. If the logistics companies do not have sufficent coin on hand to deliver to a particular bank, they will order additional coin from their local federal reserve branch and then deliver said coin to the particular branch that is ordering. Generally the only bank branches that will order coin directly from the fed are small banks, and in all my years as a roll searcher or bank teller I've never seen a bank that has.
The key to searching is volume. You may have 10 boxes in a row that produce next to nothing and then the 11th box will produce a full foll of 90%. Without searching massive amounts of halves the search becomes unproductive. Its very common to see someone search through 3 boxes and find nothing, if however you searched through 10 boxes without finding a single silver half than I would agree with you to switch source banks. The actual bank you order from has nothing to do with where the half dollars came from, its the logistic company. If the next bank you go to uses the same logistic company as the chase you currently go to, then your still going to be getting the same half dollars that you would if you ordered from chase.
A long time roll searcher will have skewed advereges because the majority of their finds will come from a select few of boxes. The majority of the silver I've found has come from 5 boxes, 3 of which I ordered at once. For example I dont even bother keeping track of my silver adverge for half dollars anymore because it would be utterly skewed by this http://www.coincommunity.com/forum/...&whichpage=1
-From a former bank teller,
Cent: 1842 (from machine) ---- Three Cent
: 1866 [Nickel] (from machine)
Nickel: 1883 (from roll) ---- Dime: 1911 (from roll)
Quarter: 1932 (from machine) ---- Half: 1917 (from roll)
Dollar: 1880 (from machine) ---- Foriegn: 1863 (from machine)