"Run Unrestricted" Saved Search Question

I've created a transaction saved search and checked the "Run Unrestricted" box. The results from the saved search include all types of transactions (Invoice, Cash Sale, Payment, Journal, etc...). When the search is ran under a role that has permission to view any transaction type (such as Administrator or CFO) the results are complete. If I switch to a role that doesn't have permission to view a certain transaction type (such as Journals) the results do not include the Journal transactions and the final numbers therefore do not match between the 2 roles.

I know I can grant View permissions to the records for all roles, and this will allow everyone to successfully run this report. However, this approach seems cumbersome and time-consuming. Not to mention possible ongoing maintenance on user roles.