During a May climb on Denali, meanwhile, you are apt to see temps around minus-20 at the 14,000-foot camp (I'm assuming a West Buttress climb) and maybe minus-30 degrees or colder at 17,000 feet. Think snow and ice everywhere, big storms, possibly days or even weeks stuck in a tent. For this you will need heavy-duty gear: a sleeping bag rated to a minimum of minus 20, expedition boots, four-season tent.
As for your gear list, though, I tend to think that the Everest ($710) is probably overkill, although it certainly would work just fine and boots such as these are commonly used on Denali. However, it's WAY too much boot for Rainier, but then, as I've implied, you're not going to find much double-duty stuff. Scarpa's Inverno ($290; www.scarpa-us.com) would work fine, better than the Everests on technical terrain, and you can get the optional Alveolite liner ($200) for more warmth. That combo would work for Rainier and Denali, as you could use the Inverno minus the liner on Rainier (although it's a little too much boot for an August climb there). Koflach's Arctis Expe ($350; www.koflachusa.com) would also work well on the West Buttress, and possibly on Rainier, too.
The North Face Inferno is a bag rated to minus-40 degrees ($650; www.thenorthface.com) that would be just dandy on Denali. Comically, it's too much for Rainier. I don't have a compromise thereI doubt there are any convertible bags that could be trimmed down for Rainier and augmented for Denali. You'd be fine on Rainier with a TNF Cat's Meow ($170), a synthetic bag rated to 20 degrees.
So there you go. You can sort of find a midpoint boot for both mountains, but not a bag. But, bear in mind that an inexpensive bag will work on Rainier. Good luck with both climbs!