I also think your plan is too much in too little time. Following are some suggestions that tweak your plans. But the suggestions to re-think and not travel as much around the country are very worth considering.
Can you reschedule your arrival from London to the morning? It will help. If you can, I'd get a car at the airport and head right to your Day 2 and leave the Day 1 time in Dublin for the end. Even if you can't reschedule, consider saving all the time in Dublin for the end, it saves having to deal with the car while you're there and/or the time of picking one up the day you leave.
On Day 2, prioiorirtize what you want, and probably go with only one stop in Wicklow, I'd suggest Glendalough. Trying for another stop in Wiclow e.g. Powerscourt) will be too much. With an early start from Dublin you can stop at Glendalough for a few hours and get to Kilkenny in the early evening.
Day 3 I'd suggest Cork only and skip Waterford. Or, drop Cork if you're more set on Waterford. Or drop both, I'm not sure they have enough interest to make a stop on such an abbreviated trip.
Days 4/5 You're not going to have a lot of time to do anything on these days but drive to your next stay. If you can squeeze another day, consider driving to Dingle on Day 4, starting early for the Slea Head Drive on Day 5 and then stay in Ennis. Or stay in Kenmare on Day 4 and start early on the Ring of Kerry (I prefer Dingle/Slea Head).
Day 6 Prioritize what you want to do to a single item in County Clare. You can probably see the Cliffs of Moher and get to Dublin at the end of a long day.
Still very full, bit more manageable. The suggestions to re-thimnk everything and stick close to Dublin are good also, perhaps combined with a day or two to Galway and a day trip out of there.