I really think you should play them as Liszt writes (with the right hand only). The quality of sound when played only with the right hand is much better than that produced by splitting the notes over two hands. It might seem uncomfortable to do so if you did not have to deal with similar passages before. You will get used to it.
If you have not played passages of this nature before, I advice you to practice them very slowly at first (in fact, practice it slowly even when you have developed speed) and articulate them clearly too. This is a very moving passage (when played properly) and it is ff. You should drive a lot of emotional strength out of that passage but never too vulgar and bombastic (it becomes what I call 'emotional weakness' this way).
In terms of fingering, I would use the one originally noted on the score (but again only play them with the right hand).
Once you master playing them in the right hand only, I can see two advantages:
1- You will realize how inefficient and un-pianistic it is to split the work over two hands.
2- You will benefit so much because this kind of passages is very prominent in advanced romantic and post romantic works. Once you get them, thats it. You will not have to think about them technically anymore (Thus you will certainly have to spend more time thinking about them but only in the musical context in which they appear). Ultimately, that's what many pianists would like to develop: utmost facility and familiarity with different techniques so that more time and energy is spent on dealing with the music itself.
No matter how advanced we are, we often face similar problems. The issue of splitting work over two hands is very common and often leads to heated discussions among particularly passionate pianists. I advocate the camp of the great Claudio Arrau, who insisted that passages are to be played as they are written and without cheating (splitting over both hands).
Of course, one can split over two hands the crazy arpeggios of the first movement of Beethoven's Appassionata, or the opening of Beethoven's Hammerklavier, or even his Op. 111. Of course you can also do that with the very confusing passages from Ravel's Ondine. But ultimately, I think it is something we should not do. Play as it is written is what both Claudio Arrau and Sviatoslav Richter advocated.
Good luck. It is a very interesting piece of music. Read the poem it is based on. I think Liszt reflects thoroughly and rather philosophically on many of the issues and feelings that the poem proposes.
Topic: Liszt Sonetto 104 Fingering Query