I've done similar trips in the Rockies, starting out with an 8,000' day (80 miles), then continuing with shorter 5,000 to 6,000' days after that. With that kind of climbing, reducing pack weight is important, obviously, and water is a critical part of pack weight. I try to plan water sources so I don't have to carry much on the big climbs. Sometimes I'll dump what I have if there's known water on the descent.
Only you know your climbing abilities and limits. I've never exceeded 11,000' in one day, and I like a rest day after that. I can sustain half that pace indefinitely--where I live that's a major pass a day with some rollers. I cycled a big pass like that every day on a traverse of the North Cascades.
I hiked over the Bridge of the Gods on my PCT hike in 2004. Loved it. Lots of rain though. I've crossed Oregon by bicycle and by foot. It's one of my favorite places. A good friend lives and cycles in Burns.