The logic of the heter makhira of chag hamatzot depends on the exclusion of the uncircumsized from the national festival.
The heter makhira implies that uncircumsized residents could in fact own chometz during chag hamatzot. Let's say that were so. That logic of a heter makhira could nonetheless not apply to the laws of sheviit because the uncircumsized are not excluded from the mandate of sheviit.
No-one can use the land on the sabbatical year because in the land of Israel no mortal owns the land and therefore during the sabbatical year no-one has title to lease it to another.