They didn’t “try” to go to a Pacific island, they actually went to one. And the Royal Navy was looking for them, but they never found them. (An American vessel finally stumbled upon the survivors, mostly native women and children, after 20 years.) So the white boys sticking out was entirely irrelevant.
The mutineers made a completely correct and logical choice, so I’m not sure why you’re trying to improve upon it.
The western coast of North America would have been a spectacularly bad choice. The Spanish, then moving north into California, were unfriendly toward immigration from outside of the Spanish Empire. Even if they had allowed the mutineers to settle, the mutineers would have had no land, no knowledge of how to farm in the Pacific Southwest, and no ability to speak the local language.
Farther north, the Pacific Northwest still belonged to American Indians, and while they may have succored people they believed to be shipwreck survivors, in return for trade goods off of their ship, the long term prospects of the mutineers would have been poor. Again, they would have had no knowledge of or ability to farm the local land, even if the Indians were kind enough to grant them a plot. And, they would always have been at risk of the Indians turning them over to a passing British vessel in return for trade favors.
An attempt to reach the eastern US, as noted, would be suicidal. The Tahitians would never have agreed to go to America, so the mutineers would have had to crew the ship themselves through formidable navigational hazards. Besides which there were too many British ships in the Atlantic.
The Tahitian men and women who accompanied the mutineers had the crops, livestock, and skills to survive on a Pacific island, and on uninhabited islands land was there for the taking. The mutineers could not have made a better choice. Unfortunately for them, they couldn’t get along with the natives, and most of the men slaughtered each other.