Keep in mind that there are nuances to different interpretations of the unitary executive approach.
Nelson's argument, even if originalist, might be in full agreement with some proposals of the unitary executive.
Just for example, consider the potential Federal Reserve limitation that the Court gestured toward, or arguments that say the president can fire anyone he wants but he can't redirect funding, or vice versa.
The originalist approach is actually pretty amenable to to those sorts of arguments of magnitude by looking at original categorizations.