To determine if it is compliant will rest in the hands of your local AHJ.
IMHO, based on what you stated, I would be OK.
A 'way around' the objections of some AHJs may be to install a single receptacle in the 4 Sq, and put a male cap on your cord w/strain relief.
If you think about what you describe...your 'scope' could only be the receptacles above the heater locations, with the client providing a 'short' extension cord to plug in the heaters.
