So can anyone recommend a solution?
If you're using IIF files (a file format that has been deprecated for about 8 years now, and which is known to cause corruption issues with QuickBooks files) then there is no solution.
You should use the SDK/Web Connector instead, as the XML API is much better supported by Intuit and includes support for linking/applying transactions.
Or should we recommend the client finally move away from the .IIF file and start using the QuickBooks Web Connector?
Yes.
Is there support for this in there?
Nope.