Solution: Apply the LCY adjustment entries only against each other (not the original invoices/payments), via Customer Ledger Entries → Actions → Application → Apply Entries, assigning the same Applies-to ID to just those correction entries, then Post Application once Balance = 0.00.
If they don't net to zero, post a small offsetting LCY journal line (Currency Code blank) against the customer to clear the residual, then apply/post it the same way.
Since Amount (FCY) = 0 on these entries, this won't touch EUR balances or bank reconciliation — just verify no unexpected realized gain/loss lines appear in G/L Entries after posting.