Companys with large mail volumes are handled differently than individuals ~ always have been ~ their carriers don't select and mark up their pieces for forwarding after a move ~ rather, that's done at a secondary distribution that used to be known as a "city case".
Think of it this way, the piece is mailed at Boca Raton post office. At the same time the terrorists buy a new pack of embossed postage envelopes. They load them up the next morning out at the park, then, that evening, drop them in several street collection boxes where they end up getting "lost in the mail" (due to a variety of quite normal operations) and travel in a stack of trays all the way to a major mailer somewhere in central New Jersey.
Those letters are then fed into the regular mailstream over a period of time as those trays are taken off the stack for use.
This explains the origin of the mail, the identity of the terrorists who mailed it, how some of it came to be canceled in New Jersey, and why it was canceled on different dates, and, most importantly, 100% of the cross-contamination that resulted in downstream infections, and in a case in Connecticut, death.
And it's also another one of your "possiblities" which when examined is absolutely ridiculous. It requires a series of accidents which would somehow cause a single batch of letters to somehow break into TWO batches of letters which would somehow be sent to New Jersey, which would somehow end up with ONLY the letters containing the crude powder somehow being sent out first, while the second batch (with the sophisticated powder) somehow sits around for three weeks until it somehow gets put into the system, too. It requires that this SERIES OF MISTAKES would somehow miraculously result in the senate letters being postmarked in the SAME area identified by the RETURN ADDRESS on the letters.
Everything you say is based upon the idea that it cannot be proven to be impossible, therefore you are free to believe what you want to believe.
It may not be impossible but it is also totally preposterous.