The sender is your problem here, not the USPS, I'd bet money on it. Note on 4/8, he sent the pre-shipment info to the USPS. That doesn't mean he sent the actual package, or told the USPS to pick it up. Chances are it sat in his office or wherever until 4/27. I don't wonder why the shipper won't answer you...he (they) know they screwed up.
Understand this, too: The USPS does not guarantee 2-Day Delivery on Priority Mail. They can't guarantee it, simply because they aren't the only people handling your package. Next time you mail a package Priority Mail, look at your receipt. It'll give you an estimated delivery day. It'll say something like "Delivery scheduled for such-and-such-a date."
Guess who flies your Priority Mail? And your regular mail? FedEx. UPS. And commercial airlines like Jet Blue, US Air, and any number of smaller feeder airlines. The postal service has no airplanes to fly mail from Point A to Point B. Zero planes. And the USPS isn't gonna put it on a truck and drive it across the country.
Guess what else? Airline planes have weight limits, just like tractor trailers. If that weight limit is reached before your little package gets on, it'll sit on the ramp until the next plane comes along...might not be for another eight hours. UPS is notorious for "hiding" mail at airports.
So next time you get all bent out of shape about slow mail service, take into account there's a whole bunch of folks you can blame for it besides the USPS.
If FedEx and UPS completely took over mail delivery, you folks would be whining and crying so loud, the sound waves would trigger a nationwide earthquake or something.