In my opinion, we model the smaller activities (OTOPOP, like EPC) in BPMN, whereas the application function in ArichMate is an IT function that resides on a higher level of detail, not showing the same amount of detail, such like a Level 2 Value Added Chain Diagram.
For example, the IT Function could be "Bill Processing - Online" where lower level activities would be, for example, a BPMN model which is named "Process Bill for Online Purchases" which is modeled with multiple functions such as
Validate customer data
Confirm complete order
Create Merchant sales statement
Send Merchant sales statement
Receive Merchant sales confirmation
Send product transfer approval
However, you are right that the Script or Service task could also be linked in the lower levels, have you tried to create assignments instead?
What about creating a Function Allocation Diagram assignment (I think this is what Jef is suggesting) off the ArchiMate Application Function object? I don't have the ArchiMate update on my instance of ARIS so I can't test it.