Is it possible to divide up the wage into a part that is wage and a part that is a free reimbursement for extraterritorial costs?
No, only an administrative division of the wage is not possible. A division in the sense that the wage is lowered according to employment law with simultaneous granting of a free reimbursement is possible. The free reimbursement should be granted along with the salary agreed.
Consequence of lowering the wage according to employment law is that any benefits which are related to the wage (like social security and pension) will be affected in a negative way. That is why it must be agreed in writing separately.