I'm wondering what Constitutional hurdles this method of voting would face in the US. The one that comes immediately to mind is the one man, one vote principle that ended the practice of at large representation in states with multiple House members. Does anyone see any other major conflicts with the Constitution?
You are wrong. One man, one vote had nothing to do with ending at-large House seats. They ended a couple decades earlier when Congress used its Article I Section 4 power to alter the regulations for choosing Representatives to force the States to use single method districting for apportioning their Federal Representatives. Nor does one man, one vote preclude multi-member districts. Indeed, South Carolina in the decade after one man, one vote came into being used a kludge where the Senate was elected from multi-county districts that had multiple members (prior to one man, one vote, the legislative delegation from each county also served as the county council, it took them a few years to decide how they were going to reorganize how county government was elected).
The main Constitutional impediment to adopting MMP for the U.S. House is the requirement that Representatives can only represent a single State. Hence to implement MMP in the U.S. House for all States without a constitutional amendment would require a massive increase in the size of the House. MMP is effectively meaningless in States that have only 1 or 2 Representatives, and even in those with just 3, it would be not particularly useful. I can't see the U.S. going to a 2000 or more member House just to enable MMP to be used in the selection of every State's delegation.