I'm sure as can be that citizens of Ireland and the UK don't need them for each others' countries
We definitely don't. The agreement between the UK and Ireland is that we are treated as citizens in each other's countries, even down to voting rights.
you ask three removal companies and you get three different answers!
Witam w Polsce ........ that's pretty typical. Btw you do know that many Polish people don't understand the difference between the Republic of Ireland and the North and therefore will not understand that you're an EU citizen (well you'd still be one anyway even if you're from the North). I had dealings with a notary last year and it took nearly an hour to persuade her that I wasn't British. She couldn't get her head round my Irish passport. Kept insisting that my passport wasn't valid because of Brexit and that Ireland was part of the UK. She finally agreed very reluctantly to proceed with the business in hand, after spending 40 minutes trying to research it on the internet.
I agree with Jon, find another company that knows what the f*ck they're doing.