I love how you specify Appendix B and the Timeline as if I'm limited to only where you tell me to look.
Where the last part regarding the Numenoreans is in Appendix A. "As a reward for their sufferings in the cause against Morgoth, the Valar, the Guardians of the World, granted to the Edain a land to dwell in, removed from the dangers of Middle-Earth. Most of them, therefore, set sail over the Sea, and guided by the Star of Elendil came to the great Isle of Elenna, westernmost of all Mortal lands. There they founded the realm of Numenor."
And also...
"Thence the Eldar came to the Edain and enriched them with knowledge and many gifts; but one command had been laid upon the Numenoreans, the "Ban of the Valar": they were forbidden to sail west out of sight of their own shores or to attempt to set foot on the Undying Lands."
Had Numenor been within sight of Middle-Earth, they would not have needed a star to guide them. Had Aman been within sight of Numenor, they could not possibly have sailed west out of sight of their own shores, therefore it only makes sense that past the sight of their own shores they would at some point have seen Aman.
Therefore, we know that the ocean is far too wide to swim and not narrow as
@Galandris was theorizing, which makes my first paragraph true. It becomes even more true since the Helcaraxe is not in the LotR Appendices, so all they could use was the super wide ocean we know exists.
The only part of my post that isn't either in Appendix A or is a result of Appendix A, is the paragraph of the drowning elves, which simply doesn't matter to my point and was thrown in as additional information.