PARTIAL SOLUTION:

The following User Defined Default

... will set the Currency of a newly created Customer Invoice for Contact with partner_id = 8 (so change this to match the ID of the Partner you want) to the currency with id = 1 (so change this to match the ID of the currency you want).

Note: Customer Invoices and Vendor Bills share the same model (account.move) so this will also affect Vendor Bills (overriding the Supplier Currency setup) except when Vendor Bills are created from a Purchase Order (where they respect the Supplier Currency default or the currency chosen on the Purchase Order) so this is a solution only if Vendor Bills are never created without a Purchase Order.