So, this started as idle curiosity and now I have 20+ browser tabs open across two devices trying to figure out the proper mutations and prefixes
I think we all can feel you there, a translation to Sindarin can turn out to be quite a rabbit hole. Considering that’s one of your first translations, it’s quit solid!
mi nirnaeth boe menof(menim?), ach û penestel
We don’t know how one should construct a sentence with boe, the only information from Tolkien we have is “I must (impersonal)”. Looking at Quenya's impersonal verbs, I'd suggest boe mened ammen “[it] needs going for us”. Also, û should cause mutation on the following word, so pen-estel → û ben-estel. It's always a bit of a question how Sindarin pronouns work, but - is from a later conception than -m, so I'd prefer it (though it should attach to men- with an -i- as well, so menif). Tolkien also vacillated on whether Sindarin distinguishes “we and you” (inclusive) and “we, but not you”, if we want to keep this distinction the former is -b while the latter is -f (and than you need to answer the question whether Arwen was included in Aragorn's sentence or not).
mí û ui'leined an i gyr en amar
“We” should be pe or me (inclusive and exclusive like above), I'm not certain where you got mí from. I think gleina- is a good choice, though I don't understand the particular form gleined, I'd translate “bound” as the passive participle gleinannen. Also, that's not entirely clear, but many Neo-Sindarin writers today interpret en as including the article, “of the” which amar doesn't need (because there is only one world), so I'd use an implicit genitive i gyr amar (like e. g. aran Moria “king of Moria” on the doors of Moria).
a din athan athan rínas
This phrase is a bit problematic in Sindarin, because “beyond” turns up both as a regular word and as part of the grammar for the “more than” expression, so I'd slightly rephrase it to something along the lines of “and beyond them is more — not only memory”. Also, “there is X” in the sense of “X exists” is a bit difficult, I usually rephrase that as something along the lines of “we can/will find X”.
I also refered to Eldamo, Thorsten Renk (www.science-and-fiction.org), and Fiona Jallings (academy.realelvish.net). For the last few words including the concepts of beyond/more I used the Noldorin word athan for "beyond" as per a neo-sindarin lesson by Jenna-Marie Carpenter (sindarinlessons.weebly.com). That also provided the abstract suffix -as to extrapolate rínas from rîn (remembrance).
Eldamo and RealElvish are both great resources and are actively maintained. Thorsten Renk's site is great as well, but he hasn't been active since around 2015, I think, so some contents of his site will be out of date by now (periodically new notes from Tolkien get published and that usually changes our understanding of the language quite a bit). Jenna Carpenter's site is somewhat problematic in my opinion it is actively maintained and right about most things at core but unfortunately riddled with errors, so I wouldn't recommend it as a learning resource. Rínas works though.
That said, this quote actually came up as a translation challenge on the Vinye Lambengolmor Discord server, which is a great community if you decide to study Sindarin further, and that was my take:
Gwannathab níreb, ach û ben-estel. Elo! Pe û ’leinennin an·uir vin Echyr Gardhon, a thar sain hirathab am — û ero rîn. Novaer!
gwanna-atha-b nír-eb, ach ū pen-estel. el[a]-o! Pe ū gleina-nnen\ī an-uir vi-in echor\ī gardhon a[h] thar san\ī hir-atha-b am — ū ero rîn. N[a]-o-maer (all mutations are removed and \ī indicates i-affection for plurals, to make it easier to disect).
“We will go sorrowfully, but not without hope. Behold! We are not bound forever [with]in the Circles of the world, and beyond them we will find more — not only memory. Farewell!”
