How do I give one party a different payment-terms grace period?

By default, every customer is considered overdue based on your company-wide payment terms, set in Company Settings under Reporting. If one party has agreed to different terms — say, 45 days instead of your usual 30 — open that party from Parties and fill in Payment Terms (days) on their form. Leave it blank to use the company default. Setting a number there only affects when that specific party is flagged as overdue for reminders — it doesn't change anything else about how their ledger or invoices work.