OK, here's a roundup for you:
Sur-i-kha/Sur-uh-kha (the final sound is very soft and not like a throat clearing sound) is how to pronounce the name no matter what your baby name books say. (This has been pointed out from the start of the thread). As Squeegie pointed out, baby name books are not reliable. As a rule of thumb if a book has any Irish names in its K section, then it should be tossed. Another thing to look out for is whether names that rhyme with Aidan are placed in the Irish category. (Just two of the many ways you can spot a name book that has been generated by some printing house software in much the same way that they print joke books.)
There really isn't that much regional variation. You are mistaking the efforts of many posters here to try to get you to understand the sound of the name, using the English language to convey the sounds, for vast differences in Irish pronunciation. Such vastness doesn't exist. (So this "there are so many variations and even with the correct spelling and pronunciation in the country of origin - I wonder if all Irish names are like this? I don't know.. I wonder if that is because this is traditional or if it is a consequence of so much traditional language being disturbed for so many generations? Don't know but it is interesting. is baloney).
In Irish the letter O is pronounced like the English letter U unless it has a fada over it, which indicates the sound is to be lengthened.
So Sor = Sur, or if you like 'Sir', as in 'Please Sir, can I have some more..'
In between the R and the C there is a schwa sound.
The letter combination CH is pronounced Kh or as in Scottish 'loch', a soft sibilant sound.
Seoirse (boy's name, Irish version of George) is pronounced SHORSHA. The Es are slender and therefore sound like SH in English.
Saoirse (girl's name, means 'Freedom') is pronounced SEERSHA or SARE-SHA depending on whether your Gaeilge is from west/north or southwest respectively.
Squeegie, I think you are right -- the name is as rare as hens' teeth in Scotland. I also agree wrt the air of arrogance.