Actually, the ship was sinking very rapidly. For a space that big to fill with water in a hair over two hours is huge.

While it's true that most of the people who were offered spots in the first 10 boats thought the ship would remain afloat, by the time the last 7 boats (three of the four collapsibles were not lowered by davits) were lowered, it was apparent what was happening. This is reflected in the capacity numbers: boats 1-10 were launched at anywhere from 5-24% capacity, while the last seven were at 92-110% capacity.

There were plenty of signs of panic on the ship. There are several reports of officers drawing pistols to keep the crowd back (most notably 2nd Officer Lightoller and 5th Officer Lowe, who both survived and related their first hand accounts of doing to so congress) and at least one record of shots being fired (Lowe again; he said he fired a warning shot along the ship's side.)

But despite the increasing desperation of the situation, there were, indeed, still many accounts of bravery among the men: John Jacob Astor put his pregnant wife into a boat, only asking for the number so he could find her again; Ida Strauss was offered a spot in a lifeboat but refused to go without her husband, Isador. When it was suggested that nobody would object to the 75 year old Mr. Strauss taking a seat, he said he would not get on before any other man. And, of course, there's Benjamin Guggenheim, who disappeared below decks with his manservant, only to return some time later dressed in their evening best. When survivor Jack Thayer asked him about it, Guggenheim replied "We've dressed up in our best and are prepared to go down like gentlemen. Tell my wife, if it should happen that my secretary and I both go down, tell her I played the game out straight to the end. No woman shall be left aboard this ship because Ben Guggenheim is a coward."