Here's one last sentence that I couldn't quite figure out:
Ach ó thosach deireadh an ghnótha do chuireas do dhearbh-dhualgas romham caint Mhaurice Mhuiris insa chruinne chéanna go bhfuaireas í a thabhairt liom sa scríbhinn gan athrú gan ceartú; is é sin le rá, faid ab fhéidir san a dhéanamh gan dul ar iontaoibh litriú foghraíochta nó gan litriú aithnidiúil na teangan a chur as a riocht an iomad.


My try at a translation:
But from beginning to end of the affair I put … ??? … in the writing without change (and) without amendment; that is to say, (to the) extent that I was able to do it without having recourse to phonetic spelling or without the familiar spelling of the language being put too much out of form.

Your translation is perfect pretty much. All that's missing is Dearbh-Dhualgas which means "solemn duty". It can also appear as Dualgas dearbh.

(Dualgas = duty)

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The dialect I use is Cork Irish.
Ar sgáth a chéile a mhairid na daoine, lag agus láidir, uasal is íseal

Okay, thanks!

* edit: What about the part that says:
…insa chruinne chéanna go bhfuaireas í a thabhairt liom …

Maybe something like: … in (with) the same accuracy that I got it taken by me …

The last sentence in the introduction that I couldn't quite figure out:
Ar shon san, creidim go bhfuil máchailí ar an dtéax ná raghadh gan ceartú roimh é a dhul i gcló, dábar go mairfeadh an té do thug uaidh é chun éisteacht leis an té do scríobh é á léamh thar n-ais do arís.

My try:
Even so, I believe that defects in the text shouldn't go without correction before it goes into print, … ??? … to listen to the one who wrote it read it back to him again.

… dábar go mairfeadh an té do thug uaidh é …

an ghnótha do chuireas do dhearbh-dhualgas romham caint Mhaurice Mhuiris insa chruinne chéanna go bhfuaireas í a thabhairt liom sa scríbhinn gan athrú gan ceartú

Okay so:
an ghnótha do chuireas do dhearbh-dhualgas romham = The solemn duty I put before myself...

caint Mhaurice Mhuiris (...) a thabhairt liom sa scríbhinn gan athrú gan ceartú = The speech of Maurice Mhuiris to bring with me into writing (literally: in the writing) without alteration of correction.

The part I have above in (....) expands/describes caint Mhaurice Mhuiris:
caint Mhaurice Mhuiris insa chruinne chéanna go bhfuaireas í = The speech of Maurice Mhuiris in the same perfection that I found it

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The dialect I use is Cork Irish.
Ar sgáth a chéile a mhairid na daoine, lag agus láidir, uasal is íseal