Database free space not being reused
Rebooting the server has fixed the issue

After rebooting Server A  the correct amount of free space was showing on the affected databases on Server A.
e.g. for the example in the question the affected database that was showing 9% free on Server A and 75% free on Server Z is now also showing  75% free on Server A after rebooting Server A.

We have now shrunk the affected databases on Server A back to having a normal amount of free space and run the imports.
The databases have only grown by the amount of new data that has been added.
e.g. if 3GB deleted and 3.1GB inserted the database has grown by 0.1GB instead of 3.1GB.

For reference Server A had been rebooted 3 weeks before and we are now planning to upgrade to SQL Server 2016 in the next couple of months.