Dean, I聮d like to direct your attention to a photo that appeared in May in the Anchorage Daily News. It depicts one , a 29-year-old woman from Spain who took a crack at Denali in mid-May. She summited, but in the process froze her feet. In the photo, you can see her purple toes聴most of which she likely will lose.
Outdoor Research Brooks Ranger Overboots

So, sure, wear your ICE 9 boots. And then ask yourself, do you value your toes? Because the ICE 9s ($350 when new, but now discontinued) are fine boots, but they聮re really not quite suited for expedition-type climbing such as on Denali. Yes, they聮re fine on a peak such as Aconcagua, the 22,841-foot mountain in Argentina. And yes, it does get cold on Aconcagua. But Denali is sort of in a league by itself, given its proximity to the Arctic Circle. Especially in May, it gets cold, cold, cold there (-25F and colder on a regular basis). I was there in June several years back and we saw -20F several times at 17,000 feet.
So I聮m with your guide聴go with the double boots, and full overboots. 聮s tried-and-true Inverno ($279) is a good choice, as is the newer and lighter Omega ($375). Also take a look at the Arctis Expe ($400). 聮s Absolute Zero overboot ($100) is a good choice, but I聮d probably go with the Brooks Ranger from ($135), as I think they are a little warmer.
So that聮s my take. Hope you have a good trip!
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