I was assured by Legislative Council Services director Raul Burciaga that the Gentle Giant's appointment would be legal because unlike a cabinet secretary position, chief of staff is not a "civil" office.
It looks like the attorney general's office agrees. House GOP leader Tom Taylor formally sought an opinion on the matter. Here's the AG's response, which basically is what Burciaga told me.
"You requested our advice regarding the constitutionality of a former legislator’s service as an employee in the governor’s office. Specifically, you asked whether certain positions in the governor’s office, such as chief of staff, legislative affairs director, press secretary and policy advisor, are covered by the prohibitions of Article IV, Section 28 of the New Mexico Constitution and whether a legislator may resign from the legislature to take such a position. As discussed below, we believe it is legally permissible for a legislator to resign from the legislature and accept an employment position with the governor’s office, as long as the position is not a “civil office” subject to the restrictions of Article IV, Section 28.
"Positions in the governor’s office like those you describe are generally considered employment positions rather than civil offices covered by Article IV, Section 28. The positions of chief of staff, legislative affairs director, press secretary and policy advisor are not created by the legislature. The governor creates the positions, controls their actions and defines their duties. A person serving in one of the positions is responsible for administering and implementing the business of the governor’s office and, most importantly, is not vested with any independent or sovereign authority of the government.
"Based on the typical characteristics of the positions you describe, we conclude that they are not civil offices and that a legislator may resign his or her legislative seat and accept appointment to one of those positions or a similar employment position in the governor’s office without violating Article IV, Section 28.1"