Everything in the SharePoint world revolves around the site collection (SPSite) and it's boundaries.
As such, when you defined custom properties from the property bag as IndexedPropertyKeys, you were able to use said properties as managed properties in search refiners, but only at the site collection level. That was evident in your results mentioned.
You could script a loop to apply the same approach to each site collection in your farm that uses the same properties, but if that is every site collection in the farm, or at least the web app, you would need to cater to future created site collections via either manual intervention or event receivers on site creation... Not very efficient. Add to that the fact that your definition of new managed properties requires a full crawl to take effect as search refiners and you're approaching rocky ground the more your data grows especially if your search administrator simply defined a single content source containing all SharePoint sites. Unfortunately, most administrators don't have extensive search experience so this problem only surfaces later on when it is much harder to correct.
Instead I recommend you evaluate what those property bag values are being used for and seek an approach that STARTS with a Managed Property instead thus reducing the need for recurring full crawls.