Thank you all for the advice. I ended up with the following:
- 1st night Holiday Inn Express Dublin Airport (25K IHG points, comes w/ free breakfast)
- 2nd/3rd nights Radisson Blu Royal Hotel Dublin (66K Club Carlson Points, pricey b/c business room that comes w/ free breakfast....no standard 50K rooms left for dates)
- 4th night in London.....had friend insisting we stay with them, so skipping hotel now.
- 5th/6th nights Radisson Blu Champs Elysees in Paris (75K Club Carlson Points, pricey b/c business room that comes w/ free breakfast.....decided to splurge for location)
- 7th night in London.....back with friend before flying out next morning.
It's going to be a whirlwind trip. I decided to throw in a mini-trip to Paris via the EuroStar train. My wife has never been on it. Excited for her to experience a train that goes up to 186mph. I've never been to Japan, so this is the fastest I've experienced so far. We're excited for the trip.....and I'm glad the hotel situation has been resolved now! Thank you for the recommendations! Haven't been abroad in 9 years; been tougher since kiddo #1 and #2 has come along.

But glad I could convince the wife to make it work. And thankful for the FT community for teaching us so much about collecting points and now, using them for fun trips!!! Thank you!
-Ryan