Nice update! I was able to use this to run a SmartThings Scene. I used the format:
$.post("https://api.smartthings.com/v1/scenes/REPLACE_SCENE_ID/execute", {}, {"headers": { "Authorization": "Bearer REPLACE_WITH_TOKEN"}})
I got the token from the personal access tokens page:
https://account.smartthings.com/tokens
And I found the scene ID from the List Scenes page when viewing the location in the SmartThings IDE. I played with the API and you can get it that way too, but I found that looking it up in the IDE was easier.