For charities in Ontario, part of the HST on an expense is recoverable and part is not. How can I configure QBO to add the non-recoverable portion to the related expense?

Currently, there is no automatic configuration to direct the non-recoverable tax portion to the related expense account. You may consider continuing to manually reallocate the amounts to the correct expense accounts.
 

By default, QuickBooks moves these amounts into a designated account to keep your tax tracking distinct and organized. Take note that changing this destination will affect your reporting and ledgers. I recommend consulting a professional accountant to help confirm if reallocating these amounts is appropriate for your business and ensure your financial reports remain accurate.
 

Please don't hesitate to reply below if you have any questions or other concerns.