The 4.3 implementation of CiviAccounts was only trying to support Chart of Accounts accounts, not projects/jobs or donors/customer oriented payments.
IIF does not allow, as you may know, a payment to be linked to an invoice or other transaction (http://support.intuit.ca/quickbooks/en-ca/iq/Import-and-Export/Importing-or-exporting-data-with-IIF-files/HOW12778.html
There may be a work-around / enhancement to support this. Looking at the attached IIF Reference.rft (renamed to .txt to allow upload here) examples, the TRNS line of the .IIF files could optionally have the civicrm_contact.display_name put into the NAME field of the TRNS line of the transaction via a customization or extension.
Amongst the issues here are that .IIF imports are quite touchy in various ways. If there is not an exact match, then additional entries are created. For example, if the name in CiviCRM (possibly as updated by user on most recent visit) does not _exactly_ match the customer's entry in QuickBooks, a new customer will be created. Once imported, it can be difficult to find and eliminate imported data in order to redo the import with a corrected file. Re-importing a file with a single changed transaction will create duplicates of all of the other transactions.