Happy feet are good
I saw several people in sandals in those pics.
Blisters from sandals shouldn't be a concern simply because they are sandals. If they fit well and are broken in, that won't be an issue.
And I doubt that the 'climbing' the mountain disqualifies sandals; uneven terrain and weak ankles are more of a concern indicating ankle support is needed than merely elevation gain. Only you can decide if you need ankle support in this instance. I backpack with very light ankle support and a 45 lbs pack, and hiking in sandals is normal for me, but I have strong ankles. If you are someone who is prone to rolling your ankle, then you probably need ankle support. the sports sandals will all have tread specific for water traction. you just need to break them in to see if there are any hot spots. I'd recommend the keen h2 style that fits to your foot with neoprene.
The thing with a trail runner is that, based on the pics, is that they look like will end up being wet most of the trip with all the streams and humidity. They might partially dry out over time, but your socks will stay wet. Your feet and socks will be wet most of the time. Wet socks on wet feet are very likely to cause blisters
I'd be more likely to go with a waterproof trail runner and an extra pair of socks that you can change into if needed.
I know you probably don't want to hear this, but you can also carry a pair of sports sandals in your pack just in case, and start off with another choice of footwear. I have done this when my boots weren't waterproof and would change footwear for water crossings.
I also take sandals along when breaking in new boots; I did some hiking in the Swiss Alps in sports sandals because I got blisters from my boots.
Cindy