I'm not sure if this suggestion is feasible or will work (not tried it myself!)...
In the Automation user guide
https://sparxsystems.com/resources/user-guides/14.0/index.html#automation, page 357, there is a FileOpen event that an Add-in can make use of.
My thought goes along these lines:
- Write an add-in that responds to this event, which does whatever task you want in the model when opened (I don't know if that can extend to running your script)
- Make your task scheduler open the model (this should be easy if it's an EAP file as the task will just run the EAP file, which will result in EA opening and loading the project). Might be more tricky if you have a database backed model
- When the model opens it should action the FileOpen event which runs your required task
- Make your task close EA (again I've no idea if you can automate that!)
As you'll notice there are a number of things in there that I don't know if they work, so, feel free to shoot down any or all of that as I've just given a suggestion based on what I spotted in the automation documentation with zero knowledge of whether it will work in practice.