This is great to have as good a reply as this but, as with all DNA testers, you should also use your DNA matches to identify not only the common names you have given but their locations - where indications of Irish origin are given. Use these collateral families to guide where you came from. With some experience of doing this you will get a better picture and it will add to the advice already given?
Where there is no evidence of location this method is invaluable and I write it here for others who might have have the same type of question or for people who get advice from you.
You should also try the Leeds Method of categorising your matches so that you form groups (clusters) of people that come from the same branch of your family - this can narrow down the work involved and also give you a reference sheet which you can use for any new DNA matches you might get.