The Philadelphia Experiment wasn't about cloacking Ships it was about sending them through a worm hole. The navy was trying to solve the problem of the fact that it takes a long time for ships to cross the ocean. Instantanious travel would have ended the German U-boat threat and give America a hudge tacticle advantage over the Japanese.
Here is the evidence that it was worm hole not cloacking device.

One test, on July 22, 1943, resulted in the Eldridge being rendered almost completely invisible, with some witnesses reporting a "greenish fog" appearing in its place. However, crew members supposedly complained of severe nausea afterwards. Also, it is said that when the ship reappeared, some sailors were embedded in the metal structures of the ship, including one sailor who ended up on a deck level below that where he began, and had his hand embedded in the steel hull of the ship.
October 28, 1943. This time, the Eldridge not only became invisible, but she physically vanished from the area in a flash of blue light and teleported to Norfolk, Virginia, over 200 miles away. It is claimed that the Eldridge sat for some time in full view of men aboard the ship SS Andrew Furuseth, whereupon the Eldridge vanished from their sight, and then reappeared in Philadelphia at the site it had originally occupied. It was also said that the warship travelled back in time for about 10 seconds.

Many versions of the tale include descriptions of serious side effects for the crew. Some crew members were said to have been physically fused to bulkheads, while others suffered from mental disorders, and still others supposedly simply vanished.

Isn't this the effects of going through a wormhole not cloacking. The ship didn't just vanish it moved and crew members were warped around the ship.