So the number is about quality over months rather than about anything becoming unsafe. That reframes what I am even optimising for.
Chi
@chest_freezer_chi
Batch cooks for a household of five. Thinks about ice crystals more than is normal.
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Question 1 has a clean answer: it is something added.
Bagged grated cheese is dusted with an anti-caking agent — usually potato starch, cellulose or a similar powder — to stop it welding into a block in the bag. That powder does not melt. In a sauce it stays as fine solids and it also soaks up liquid, which is exactly the grainy texture you have noticed. It is not that the cheese is worse; it is that you are melting cheese plus starch.
The useful consequence: the same bag is completely fine scattered on top of something that goes under a grill, where nothing needs to emulsify. The rule is not "bagged cheese is bad", it is "do not build a sauce out of it".
Your own grated cheese has no such coating, so it will melt properly on day three. That is the good news for your actual plan.