Alternate routes of Fellowship from Rivendell to Mordor

[Tuor of Gondolin]

Since first reading LOTR and looking over the ME map I've speculated on several seemingly viable paths from rivendell to Mordor.
1- following Bilbo's route to Esgaroth, then River Running to the Sea of Rhun forest or mountain area and then using horses for a quick (obviously dangerous) dash to the Ered Lithui (perhaps disguised as eastern cavalry?

2- Go west to the Grey havens. Borrow a ship from Cirdan (no problem for Gandalf) and hug the coast down past Isen. (obviously too dangerous to go further because of Corsairs of Umbar). Fellowship then splits, Gandalf (with Merry, Pippin, Legolas and Gimli to contain Saruman and help Rohan, while the rest head across South Gondor (perhaps helped by Prince of Dol Amroth. [Gollum would meet up with them in Ithilien?]. Given that Saruman had no navy, wouldn't that be the safest and quickest way to approach Mordor?
P. S. I'm sur Tolkien could have worked in Lothlorien and Moria in some way.