Chasing money is awkward. But you are a business, not a charity.
Step 1: The "Did you see this?" (Day 1 Overdue)
A polite nudge. Assume it was a mistake.
Step 2: The "Work Paused" (Day 7 Overdue)
"To avoid further delays, please settle this invoice so we can continue to Phase 2."
Step 3: The "Late Fee" (Day 15 Overdue)
Re-send the invoice with the late fee added (as per your original terms).
Step 4: The "Final Notice" (Day 30 Overdue)
"If payment is not received by [Date], we will refer this matter to a collections agency."