As far as I can tell, there is no way to "lock in" a specific time frame on a Perfstack widget when embedding a project on a Classic view. It doesn't seem to use the saved time period from the project (looks to default to 7 days?) and if you change it then it might be a completely different time period the next time you come to the page.
When editing the widget/resource, there should be a section for default time period. A user will still be able to change the time period by clicking the option on the widget but this defined time period will be the default when the page loads.
If you add a Perfstack/Timeseries widget to the new Modern Dashboard, there is an optional setting for this time period. The Classic Dashboard widget should have the same option.