good post.
The Irish Republic does indeed sound like a self-declared area which is not a real country at all.
I met a Ukrainian woman a few years back and she absolutely HATED her country being called 'The Ukraine' and made no apologies for it. If I ever said it she retorted by saying 'The Ireland' and on hearing the stupidity of that I refrained and called her country by it's name instead of putting a prefix to it!
Although I never went into dept about why she hated it or how it came to pass your explaination above makes sense.
EDIT -
Source -
Wikipedia
In English, the country is sometimes referred to with the definite article, as the Ukraine, similar to the Netherlands, the Gambia, the Sudan or the Congo. However, usage without the article is now more frequent, and has become established in diplomacy and journalism since the country's independence.