Cross-currency payment double-entry

Design the double-entry postings for a cross-currency PAYMENT (not a balance conversion): a sender pays 100 EUR and the recipient receives USD, settled through your own FX inventory. Per-currency the books must each balance to zero, the FX spread must land in a P&L account, and the system must handle ~7,000 such payments/sec while staying auditable. The subtlety: a single user-facing transfer touches two currencies, so 'debits == credits' can't be checked across currencies, only within each. How do you structure the entries so each currency balances and the FX gain/loss is captured exactly?