I spent a lot of time reading through the tpclient-pywx code and tp's client libraries to figure out how a client sends code. This line under StateTracker's ChangeOrder method threw me off for a while:
evt = self.application.cache.apply("orders", "change", self.oid, node, order)
I guess the function of the cache object is rather self-explanatory. It is found in the tp client library, and stores all of the universe objects which has been very handy for getting object properties so far. Thinking I could use the cache.apply method to send orders (my reasoning was that when cache is changed it will notify the server automatically) I tried adding this to my code. However, nothing happened and I couldn't figure out an alternative approach and instead kept combing through the same code over and over to look for any mistakes.
When I tried downloading all the alternative clients I found the answer in the text-based python client. The code is spread over two files only, and immediately reveals that the Connection object should be used instead. It contains all the methods (such as insert_order) necessary to make things happen.
I guess the lesson learned here is to look for simple alternatives before going deeper down a chosen path. Since the tpwx client and tp client libraries have a very large code base, I should have made sure there were no other choices first before delving in.