If you enjoy the idea of discussing how to translate (poetry in particular) I can't recommend enough "le ton beau de Marót" by Douglas Hofstadter of "Godel, Escher, Bach" fame. It explores various approaches to translation, discusses a lot of funny stuff and has a zillion different translations of the same poem, which is pretty entertaining tho it gets boring after a while.

And interestingly enough, the Italian version of GEB contains a pretty horrible, in my opinion, translation of the Jabberwocky, where the monster name is translated as "mascellodonte", which seems academic and dinosaur-like rather than fantastical as the English one.

How is this for title + first verse:

ガヤ暴禽 （がやぼうきん、Gayabōkin）

見ぐれだ。にょばトーブが、

みずんがでごろぐーんと。

ボロゴーンが見ま目ま、

奪い狩るネズモン。

Gayabōkin

Migureda. Nyobatōbu ga,

mizunga de gorogūn-to.

Borogōn ga mimamema,

ubaigaru nezumon.

Title explanation:

- jabbering is ガヤガヤ, so I took half of that.

- bōkin is a play on mōkin (猛禽) which refers to a fierce bird of pray. I replaced mō (猛) which refers to severity, extremity, ferocity with bō (暴): violence, force, to create a new word.

Other notes:

見ぐれ (migure) is supposed to evoke twilight by association with みる (miru, seeing) and 夕暮れ (yugure): twilight. So that gives us the counterpart for "brillig".

にょば (nyoba) is a onomatopoeia similar to nyoronyoro: wrigg.

みずんが (mizunga) is a portmanteau of mizu + unga (water + canal). That gives us a made-up word that evokes some kind of wetland setting corresponding to "wabe".

ごろぐーんと(gorogūn-to) an invention that hopefully evokes gorogoro: heavily rolling. This is our "gyre and gimble".

ボロゴーン (borogōn) is inspired by borogove.

見ま目ま (mimamema) is our "mimsy". 目眩 (memai) means dizzy.

ネズモン (nezumon) is from nezumi: mouse. This gives us "mome rath".

奪い狩る (ubaigaru) is a made-up compound nouned verb: 奪う (ubau) is to snatch, steal. 狩る is "to hunt". E.g. 魔女狩り (majogari): witch hunt. This is our "outgrabe" candidate.

The OP missed another translation included in GEB by Naoki Yanase (a guy who translated Finnegans Wake into Japanese, which tells something).

I absolutely loved this discussion.

It reminded me a lot of the time I watched Beavis and Butt-Head on MTV in amazement in an Izakaya in Kanazawa. It boggled my mind that someone could translate the clever vulgarities and the double entendres (often enough) into Japanese. Truly a labor of love.

I find this a bit of an odd example, but maybe I am completely preoccupied by translations of technical texts, where clarity is important and staying exact at the same time. I've hardly come across words that were so foreign and weird that you'd be thinking very long if the "normal translation" was ok. This poem especially seems to be an exercise in crypto linguistics, most of the time trying to figure out the original meaning first, and then finding some fitting translation, with a task that seems more like writing a poem on your own and less "translation". But as I said, maybe it's me thinking about howtos and manuals.

Disclaimer: I have no professional experience as a translator, just a software developer who writes READMEs and technical documents in German (native) and English and has also translated stuff in the past.

My attempt at this is now hosted here.

http://www.kylheku.com/~kaz/gayabōkin.html

Enjoy!