Nowhere on the internet is this specific problem or a fix for it mentioned, so here goes:
My app contains the following doGet() and doPost()
doGet()
doPost()
I think this is somewhat expected. When one does an HTTP GET the parameters are passed on the url. When it's a POST they go on the payload, not the url.
HTTP GET
POST
Try calling post like this (Apps Script code):
UrlFetchApp.fetch(scriptUrl, {method:'post', payload:'param1=value1¶m2=value2'});