I.e. If I wanted to re-implement this myself what would I need to do?
I think you should hire Peter Todd or ask him what to do. 
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but still dont know how open timestamps actually works.
Hmmmm... Have a look to https://app.originstamp.org/home
Let us call it "close timestamps" contrary to "open timestamps"
I think it is not very hard to compare these two projects and understand the technique.
If no, you must give up and switch to something else.