I think the movie is the 1977 USA/Japanese co-production The Last Dinosaur. Rankin and Bass (of Rudolph, The Red Nosed Reindeer fame) financed it. Your description of the ship matches well the Polar-Borer that takes the explorers through the Earth's crust to a prehistoric land in the Artic. Did the ship look like the one in the pictures below? The dinosaur does attack their ship at the beach and carries it away in its mouth, stranding them on the island.

The Last Dinosaur is a color movie. The effects are very much in the Toho style. The T-Rex is a very unconvincing man-in-a-suit. That is why you may associate the dinosaur with Godzilla. The movie never played in movie theaters in the states. I remember watching it repeatedly on network and local television in the late '70's and early '80's. It has a largely American cast, so the lead actors speak their own lines without dubbing.

Richard Boone stars as an oil tycoon (and big game hunter) who finances a scientific expedition to explore a recently discovered prehistoric land at the North Pole. A very active volcano has kept the area a tropical paradise for millennia and it is inhabited by prehistoric creatures and cave people. Both attack the expedition. Boone becomes increasingly more savage and threatens the other team members. All he wants to do is hunt and kill the last T-Rex on Earth, while the others want to recover their ship and escape. Joan Van Arc (from television's Knots Landing) plays the lead scientist.

The original, un-edited cut of the movie has been released on DVD. I found two good reviews of those DVDs here and here.

This is Age of the Great Dinosaurs (1979).

From TV Tropes:

Daikyouryu no Jidai (Age of the Great Dinosaurs in Japanese) is a rather obscure fantasy/adventure anime film distributed by Ishimori Productions and Toei Animation. Directed by Shotaro Ishinomori and Hideki Takayama, it was released in 1979, and narrates the story of a trio of kids (Jun, Remi and her little brother Chobi) from modernized Japan who still treat nature with respect and conscience, unlike many other humans who pollute Earth and damage the planet a lot every day.

One fateful night they are summoned by an unknown alien intelligence who tells them that mankind is losing its empathy, and, to teach them a lesson about life, death, and the fall of species, said alien intelligence transports the kids to Earth's past and leaves them right in the Mesozoic era, the time when dinosaurs were the supreme rulers of the Earth. Here, the trio has a series of adventures and misadventures, like befriending a baby Triceratops, trying to escape from a dangerous Tyrannosaurus rex, witnessing the Cretaceous extinction and rise of the mammals, and discovering why it is important for humans to protect Earth before it's too late.

As mentioned above, the film is very poorly-known, and only a few home releases are known. It can be watched for free online, but is usually found in a foreign language, like Spanish.

Alas, Poor Villain: The Tyrannosaurus eventually gets speared to death by the Neanderthals, though this becomes sorrowful considering it's the Last of Its Kind.

The main male protagonist has dark hair and wears a dark blue top, similar to your description. And you can view the T-Rex being killed by numerous hurled spears right around the 1:01:35 mark in the video below.