Okay Salty I did some research on the swing in question.
It says unfinished hardwood.
I looked on line to reassure my self about Cypress which is what it is made out of.
Even though cypress is considered a hardwood it is a softer wood in structure.
The wood from old growth is pretty good at weather resistance but new growth not as much.
But it is a good wood and is far better than some oaks like red oak.
It just so happens I have spent a ton of time doing research on the strength of woods and bolts in the last day or so.
And things like moments of force on angles and so on.
I have to say wood is a bugger to calculate because it isn't all the same due to grain structure and things like knots and so on.
Also the way the grain is turned.
So I cant just say go down and buy a 2X4 and it will hold so and so weight.
As for hardware they have gone over the top in safety as far as what to use.
The hangers are rated at 500 lbs per hanger there are two so it is 1000 pounds total.
Some of the others are de rated big time.
This is because people will be sitting on them.
This is crazy.
Just look on line at home depot for porch swing hangers and you will see what I am talking about.
Law suits rule the world.
Back when you and I were kids they would sell s hooks and J hanger bolts to screw into a 2x4 with dag chains.
Not anymore.
If they do they are rated at like 150 pounds.
The same eye bolts they used to sell now say not rated to support people.
Here is a link to turned wire eye bolt load limits.
A 1/2 turned eye bolt working load limit is 200 pounds.
They also say to never load at an angle.
My how times have changed.
https://www.google.com/url?sa=t&rct=...1gkbhIfAlZlGhA
You say you weight 200 pounds.
If you were sitting in the middle of the swing your weight would be supported by both bolts.
If you were under one of the bolts it would be supporting all of your weight.
Now the part that is weak is the turned eye not the bolt itself.
A 1/2 grade 2 coarse thread bolt has a proof load of around 7800 pounds.
I wish I had my bolt book I left up there.
Now lets get to the wood.
I may or may not would use the landscape timbers to do this.
Reason is what I said earlier.
If you look all of them are the center of a log.
One thing to consider it where the hangers would be at.
It would be at the ends so the support would be stronger there than in the middle.
Theoretically if it would hold up 100 pounds in the middle it would support 200 pounds halfway to the end from the middle me thinks.
Here is a little project I have been working on to lift a 1000 pound weight.
Not finished yet but each square represents 6 inches.
None of the other dimensions are exactly right but I needed to do a drawing to calculate some things.
But it will show you how to support the structure you are thinking of building.
A little over board but I know you have your families safety in mind also.
Worth
Gantry hoist.jpg