Matts:
It is late, so I'll be brief.
Ireland is a rather small island, but you know it isn't as easily travelled as a state in the U.S. I'd look at regions.
ULSTER: Royal Portrush, Royal County Down
AROUND DUBLIN: Portmarnock, K Club, Druid's, Royal Dublin, Island
SOUTHWEST: Old Head, Ballybunion
WEST: Lahinch, Carne, Waterville, Doonbeg
(These may not be 1- comprehensive, or 2- entirely accurate. I'm just going from memory.)
I'd resign myself to NOT seeing all of their best courses on one trip. You can't do it and have a workable trip. Newcastle, NI to Lahinch would be a hellish drive to try "in an afternoon".
My suggestion? Since you are flying into Dublin and departing Shannon, work a loop around that part of the island. Doubling back might be tough. You've already done a great job gaining access to some of their best courses. I've played RCD and Portmarnock on your list. I'll get back for Ballybunion some day.
Sorry to see that you are missing one of the greatest places in the world to vacation. The north coast of Ulster has The Giant's Causeway, Bushmill's (the world's oldest distillery), the Carrick-a-rede rope bridge, the Dunluce Castle, and Dunsvarrick Castle ruins all within a few miles of each other. I've heard others on the board speak of Portstewart, another very good course close to Portrush.
Since costs are a concern, don't be shy about playing a lesser tier of courses - at least as far as their prominence in the United States. They have several worth seeing outside of The Big Four.
Lastly, since the best part of any trip to the 51st State is spending time with the people, why would you want to spend time driving so much? After golf, an eve in the local pubs is an experience second to none. I guarantee you could walk into a pub, buy a Guinness, and strike up a conversation with the natives at the bar. You probably wouldn't have to buy another pint all night.
Enjoy. I'm jealous. Just another place I won't be getting to this year.