Need Cantilever requirement for Saucer Swing on swing set. If I use 12x4x6 can I have an angle support resulting in 3.5’ unsupported (8.5’ supported)?

Question

Need help determining the appropriate length for cantilever on a swingset. Rough draft is below. All construction is 4x6. Looking to mount 12 foot beam on top of existing swingset beam. 5 feet would be directly on top of existing beam. 3.5 feet would be supported by a wood angle brace leaving 3.5 feet unsupported (30% of the beam). The swing is a saucer/nest type and 40 inches wide. It supports up to 330 pounds. Requirement is to mount it with a single swivel mount (allowing it to swing In all directions) so it needs to be mounted 6 feet out from the vertical post. Mount would be 1 foot away from the end of the post. Need to know:

1. If the 3.5 feet of cantilever is safe.
2. If the 1 foot between the mount and the end of the cantilever is safe.
3. If the wooden angle brace is ok at 2.5 feet down on the vertical mount and 3.5 feet over on the horizontal mount. Do not want to go too low on the vertical as adults might bump their heads.

Below is a rough draft for reference. Thanks!

Answer 1

Perhaps a truss above from a short post and some wire can provide better trade offs, especially spreading the load and avoiding the headroom problem.

However you'll probably need some significant additional diagonal bracing, more than in your drawing, to prevent the whole structure from skewing over when 330 pounds are swinging heavily in the left-right direction in your drawing.