I am from Louth and from what I have gathered, the dialect of Irish spoken here has historically been the Ulster dialect, so that is what I would preferably like to learn.

true but there are differences between the different areas of Ulster and Louth Irish wasn’t identical to the Irish of Donegal — which is the only place in historical Ulster where Irish is still alive as a traditional language (elsewhere, people are learners).

One thing that I have notcied is that the Irish I learned in school, in Louth, can sound quite different from how others pronounce it.
For example:
“Dia duit”, to me, has always been pronounced, dee-ah dit, or dee-ah ditch. But others I have spoken to and heard have pronounced it as dee-ah dewit. (Please excuse me for using basic pronounciation aids, I have no understanding of the International Phonetic Alphabet)

In Ulster it would be said, roughly, “jee-uh ditch”.
I’m not aware of any dialect that would have “dewit” (if I understand properly what prononciation you mean).

Would I be better off starting from the ground up and ignoring my previous teachings?

yes. School Irish, afaik, is never close to Ulster Irish, except maybe with some teachers in the Gaeltacht…

Also, as an additional question, how likely even is it, that the dialect of Louth Irish was similar to that of the modern Donegal Ulster Dialect? Perhaps I should just learn the Connacht or Munster dialect.

For sure, Louth was closer to Donegal Irish than to Connachta or Munster Irish. But it had peculiarities, I think there are books that describe what was Louth Irish like when it was still spoken…