If I remember correctly, Irish is derived from a different family of Celtic/Gaelic languages than Welsh, so any relation should be pretty remote and more a matter for scholars to discuss.

Tolkien states the Black Speech was artificially created by Sauron for his subjects, as you say, using Elvish elements. However, as the incantation on the One Ring was in this speech, and had considerable power, the artificiality and banality of the Black Speech is questionable. Furthermore, listening to the Orks speaking in Common Tongue, it is obvious that they have no honour and any agreement made with them is but of little value. Any magic texts in such a language would be ridiculous. How much more would it be so in the Black Tongue? Any Language which Sauron could imagine (unless specifically made to deceive) must be laden with abuse and vulgarity. The text recited by Gandalf, however, has a certain power and beauty and certainly does not smell of mockery and vulgarity. Tolkien, as a philologist who was very receptive to the beauty of words (hence his affinity to Welsh) must have noticed this. I know I'm on very thin ice now, but may I suggest there is more to the Black Speech than Tolkien admits?