Which foreign workers in USA who send remittances to family are getting the best bang for their buck?
A good start would be The Economics of Migrants' Remittances by Hillel Rapoport and Frédéric Docquier. They both work extensively on this topic. In this paper, they review the  theoretical  and  empirical  economic  literature  on  migrants' remittances.

They review six theories decomposed into two broad categories individualistic motives (altruism, exchange, inheritance, and the strategic motive) and two types of familial agreements (on insurance and investment).

In all of these six theories, except one, migrant's income is indeed a very good predictor of remittances. However, other motives matter and may differ across "foreign national workers grouped by country of origin". For instance, some societies are more altruistic than others, and assuming  that  altruism  decreases  with  time  of arrival, the size of remittances should be negatively related to this variable in the altruistic case. 

They also predict contrasting effects concerning the distance from family. For instance, in the inheritance theory, the amounts remitted are expected to be closely related to the probability of receiving inheritance in the origin country. If, as they assume there is a negative correlation between the distance from family and the probability of receiving inheritance, a Mexican worker will remit more than an Ethiopian worker, other things being equal. This could even be true if the Ethiopian worker has "the most income per capita after living expenses".

To sum up, migrant's income is a crucial variable but other variables, which may differ by country of origin, may also be of first-order importance to understand remittances.