If you can do STP in a day and back to back 100 mile rides you should be fine. I see that they moved the ride up this year so you don't have much time but it wouldn't hurt to get a ride or two in before that with some long climbs. Sunrise side of Rainier has lots of good climbs. Crystal Mountain, Cayuse, Chinook, Sunrise and even Paradise from the Stevens canyon side.
I've never done the whole CHPC but I've done the climb from the Iron Creek Campground to Windy Ridge and it is a pretty moderate grade that you can spin up. The only time it gets steepish is when you turn off FS25 onto FS99 were is kicks up to that 7-8% range for a bit. Can't remember how long but it passes quickly and eases again.
The climb itself is spectacular IMO and is well worth the drive just to do that. I wouldn't drive down there to do a "lower" loop since the scenery isn't that great.
Pacing and of course staying hydrated if it is hot is the key. 114 miles is no joke.