System, assemblies, and methods for heat shrink sealing open-topped containers wherein the system includes a two-part housing or enclosure wherein a majority of a bulk roll of film material is accessible when the cover is open. The system preferably includes a movable feed roll to improve the efficiency associated with reloading operations. In a preferred aspect, the system includes a movable sealing unit that accommodates use of the lidding system with open ended containers having various sizes and shapes. In a more preferred aspect, the system includes an indicia generating device operable to label sealed containers and a knife that generates a perforation in the film during sealing operations.