Thanks for all the insight. Below is the owner's response to your concerns.
BTW, I created an animated GIF of the entire process, as I see it, but I can't get Flickr to show the animations since Flickr turns an animated GIF into a static JPG.
I'll post the animation separately, if I can figure out how to preserve the animation, but here is the starting point static JPG: https://c2.staticflickr.com/6/5605/15466740929_084969faac_z.jpg
Here is where we are right now: https://c4.staticflickr.com/8/7575/15629669196_d8ed414ac3_z.jpg
And here is the penultimate ending point static JPG: https://c2.staticflickr.com/6/5600/15466738719_4866bb66b1_z.jpg
Here's the owners response to your valid concerns ...
I wonder if they realize how huge the final redwood tree is? The tree probably weighs in excess of 2,000 tons, and has a 30 foot circumference. The smaller set of redwood trees I would estimate weighs 15 tons. In a wind of 50 mph, the small tree experiences 200,000 pounds of force due to the wind. The idea that 28,000 pounds of tension on a cable is more than it encounters in a light wind does not seem tenable. The root structures of both trees routinely handle much larger forces during a typical day.
A wind blowing at 100 miles per hour generates 25 pounds of force per square foot. If that wind were blowing straight down on 800 square feet of deck, we'd have 20,000 pounds of force. I consider that unlikely. :-)
Edge-on, we have 67 square feet, or 1,666 pounds of force. But that is also somewhat unlikely.
Sideways forces will add a little to the cable tension, but will mostly be taken up pushing against the trees and the support posts.
The deck will weigh in the neighborhood of 5,000 pounds, and has 800 square feet of maximum surface area. Lifting that, requires 6.25 pounds per square foot, or a wind speed straight up of 50 miles per hour. But the deck is held down at the ends and in the middle by either trees or posts, which also limit the amount it can tilt or twist. The surrounding trees limit the wind considerably.
The assumption that the engineering is "seat of the pants", or that the mathematics have not been done is incorrect, but the ideas are all good because I don't want to miss something, by not thinking about it at least.
Let them know that I appreciate their advice! (Please invite them to lunch on Wednesdays in Redwood City if they're local.)