It looks like the ads cost / lifecycle stage will always be a moving target 
Here’s the response from support:
I checked our KB here on this and in relation to Cost per MQL, SQL or Lead, it is advised it is the money spent on the ad divided by the number of attributed contacts that currently have that specific lifecycle stage. Since it specifies that is it for attributed contacts currently in that lifecycle stage, the data would then be subject to changes if the attributed contacts are not in the stage anymore.
From what you mention, it seems that you would like to see the cost for contacts that have ever been an MQL, SQL or Lead, rather than contacts that are currently in that stage.
The data in the Ads campaign performance is automatically generated by HubSpot and I am afraid that there isn’t any setting where this can be changed.