You don't tell us how big the room is, but with that vaulted ceiling it appears to be the correct fan for the room.

Um, (1) how big is the current fan, and (2) do you really need the fan in this space?

Why do you want to go with a bigger fan?

Is the existing fan not moving enough air or do you just want the look of a larger fan in that space?

From the photos that you have provided it doesn't look like you would have any problems with the recessed lights creating a strobe effect if you chose a larger fan. However, that is something that you should consult with your licensed electrician and/or lighting designer before you invest in a 70" ceiling fan and installation.
Best of luck with your project.

sorry, i forgot the dimensions. H = 12' @ walls & 16' @ tallest. ~ 24'x16' L/W.

Current fan is 52".

We would like something with the appearance of a bigger fan and we would like to move some more air in the summers. Whimpy is the way my wife explains it. I worry it may overtake the skylights? We try not to run our A/C here in the foothills near Denver, so some moving air is nice during the hottest part of the day.

The movement of air for ceiling fans has more to do with the pitch of the blade than the diameter of the fan. In addition, you might want to mount the new fan on a longer downrod to help mix the air in the room.

Your room is 384 sq ft. so a 54" +/- fan should work. Click on chart.

Based on this chart below your downrod should be longer. At least 48" long.