What is the best adhesive to use for attaching nylon webbing to acrylic?
Gluing on structural straps is an iffy project for most materials.  Have you considered pop rivets? The tool can cost less than $10 and the rivets a few dollars more.




You just drill a small hole throught he plastic, punch a small hole through the strapping, insert the rivet through the holes, add a washer on the webbing side and operate the tool.  You may need two or three per attachment point, depending on how much strain they will be under.

The rivet tool may come in handy on other projects, like repairing your Tricorder.