I appreciate your confirmation that you're using QuickBooks Online Advanced, Dan. The Reclassify Transactions tool is exclusively available in this version and in QuickBooks Online Accountant. Only the Primary or Company Admin role can access this feature.
Assigning the Reclassify Transactions feature using the custom user setup isn't possible. For now, the only option is to make them a Company Admin. I'm adding a sample screenshot for visual reference.

Please know that this will give them full admin-level permissions, which include the ability to make other significant changes to your company file.
If you have any more questions, let us know. We're always here to assist.