I have recently moved into a house and sharing expenses.
The owners keep food out 24/7 for their large dogs and they feed them only Ol Roy. It is impossible to keep my dog from eating from their bowls of food.
I have always fed mine Iams or Merrick. Now he is eating this Ol Roy.
You are in a hard spot. If you cannot get some agreement about feeding times (and it sounds like that isn't an option), then I recommend supplementing your dog's diet with a little BARF.
Some raw bones and a nice little hypoallergenic dog food patty would probably keep your dog healthy and s/he likely wouldn't over eat on the cheap stuff.