Hi Nick,
I am sorry you are experiencing problems with xml import. If a query takes too long to run, or too much memory, or too much cpu power, the shared hosting server may kill the process.
You may try WP All Import and reduce the number of records per iteration until the script can run. some users have reported success on shared servers using WP all import. WP All import breaks up big files into smaller ones to speed up the import process. it is worth trying.