Hi,
there is a similar discussion here (although about starting from journals) but it seems that two Dynamo versions might be a problem:
Have you tried uninstalling one of the versions?
Another solution I have thought of would be to assign a keyboard shortcut to the dynamo command (even manually in the UI) and then emulating those key presses by the script. Should be doable.
For the second part of your question I have unfortunately no experience with startup scripts, but have you tried it as a both application and document macro? There might be a difference.
https://knowledge.autodesk.com/support/revit-products/learn-explore/caas/CloudHelp/cloudhelp/2014/ENU/Revit/files/GUID-468D3029-11FF-4C1D-BBCA-AE1C66C5E028-htm.html