Factory can definitely wait, given that you're playing as the Koreans.
By focusing on the armoury and your shooters, artillery, tanks, and healers, you might minimize the need to upgrade mills before getting those troop upgrades.
Get the upgrades on the war academy and the mercenary camp too. You get to unlock the decoy tactic by upgrading the war academy - would be a great value addition to your tactic composition in wars.
Also, getting the mercenary camp upgraded would mean you can run with Flampanzers.
These are far more valuable to get on priority during this discount, without having to wait for mill upgrades, given that you've just reached IA.
Also, if time permits, begin your barrack upgrades. I might suggest keeping these towards the end of the discount period, after you've initiated the other upgrades, just before the discount ends. Otherwise, you'll have a hard time gathering resources if your barracks are down for upgrades.
Just when the discount period is about to get over, initiate the upgrade for one barrack, then, gather all of the food needed for the next two barracks, and initiate the upgrades for the last two barracks simultaneously.
The reason I'm suggesting these is that, coming from EA, your food storage capacity would be 6 million.
During this discount period, you'll be able to initiate the following upgrades without upgrading your mills (costs after considering 40% discounts, without even having the Notre Dame):
Armoury: 3 million
War academy: 3 million
Mercenary camp: 4.2 million
Barracks: 3 million
Tank: 4.2 million
Artillery: 4.2 million
Shooters: 3.3 million
Supply truck: 4.2 million
Without taking advantage of this discount, you'll end up having to upgrade each mill for an extra storage capacity of 500,000 each, lasting 5 days.
So, I would highly recommend prioritizing armoury, war academy, mercenary camp, troop upgrades, and finally, the barracks during this discount period.
Hope this helps.
Cheers and happy gaming!