How to replace a live connection with power bi dataset

It is possible, yes.

1. Create a new blank .pbix file that you link to your SSAS model.
2. Save the file as something you will know is the main source, my test file was called 'Master_Data'
3. Publish this to your workspace.

This is the source that all your reports will use as their source.

Next you will need the PowerShell script from this article.

https://powerbi.tips/2020/05/hot-swap-power-bi-report-connections/

It strips out all the connections from an existing .pbix file.

When you run the script you will be prompted to select a file, that will be one of your existing reports you want to swap over to the new dataset.  I suggest making a copy of the report to start with for testing.

It will then open the file and all your visuals will be broken:

Now got to Get Data > Power BI datasets and choose the Master_Data you published in the first steps (or whatever you called it)

Then click 'Create'. 

If it all works your visuals should populate and all be linked to the new PowerBI dataset.

Your reports all point to the single PowerBI Master_Data set and that points to your SSAS.

This is exactly what I needed.

Many, many thanks