It can be a challenge to eliminate Siberian squill. Digging and thinning by digging is one option, and you can continue to use this in combination with some other methods to slowly reduce plant numbers.

You can mow after flowering - or somehow remove the flowers before they go to seed. Squill can spread readily via seed. 

Another options is to very carefully use a broad spectrum herbicide such as glyphosate to control it. You can spot treat making sure not to get the herbicide on any wanted plants. I would look for one of the precision gel or foam-type applicators so you can be very precise with what plants you apply it to - and always follow the directions on the label! However, even this may not be effective unless used in combination with other methods and over the course of a few years. 

More information about Siberian squill can be found here: https://www.misin.msu.edu/facts/detail/?project=&id=269&cname=Siberian%20squill