I need to access this data programmatically via API for automation. I want to automatically insert the payment into our ERP. I can do this now (requesting all invoices via API) , but it would be incredibly inefficient as time passes.

If I could get a list of payments via API based on the date the payment was processed, and if the returned data contained a list of invoice IDs, I could then apply the payments in my system without having to hammer your API.