One solution is making up for rising transaction costs with lending. Someone reliably transferring money can just as reliably service a loan.
Suppose an American is sending $100 three times a week to Mexico. You lend the American $1 200 at the beginning of the month. This is sent to a Mexican bank with instructions to disburse, in $100 installments three times a week, to a beneficiary. The American, instead of sending money to Mexico, services the domestic loan. You retain a lien on the funds deposited in the Mexican bank, which would revert to you in the event the American defaults on their loan. Similar cash flows, one international wire.