I make stuff and freeze in ziploc bags, so everything can lay flat. I have also raised the shelf in the freezer and added another wire coated shelf (like this
Storage Solutions Stacking Shelves Set of 6 - White (Medium) : Target )
I will ladel soup into a ziploc and lay it flat on it's side to freeze. Likewise have carefully loaded lasagna, baked spagetti, enchildas, casseroles, etc, etc into ziploc bags. When I get a good deal on chicken I've been known to freeze it on a cookie sheet and then once frozen load into ziploc bags. I've also flatted chicken, seasoned it and frozen so that prep time is less when I use it. I cook great deals of hamburger meat and then freeze on a cookie sheet, then load into ziploc bag so I can pull out a single cup of alredy cooked ground beef for whatever receipe. Likewise I do this with chicken so I can always pull soem out to put shredded chicken into quesodillas or top off a salad or it's ready to go to make chicken salad sandwhiches, etc.
I almost never keep anything in it's orginal packaging before it goes into my freezer, almost a full 90% of everything has been repackaged. I also then use my ice cube bucket thing to sort and organize seeing that two trays of ice cubes are more than enough for this family.
We do have another small freezer, but it's a small one, like the size of a dorm refroigerator it's just all freezer thou. Can you find a place to stash a small freezer like that? ( like this -
GE - 5.0 Cu. Ft. Upright Freezer - White - FUM5SNWW ) We got ours on freecycle and it's not nearly as nice btu I see these on Craigslist from time to time for like $50.
I mainly use this one to store and freeze excess from the garden, things that we can not can, but do freeze well, or if I get an amazing sale on something. But mainly most everything fits into the freezer atop the fridgerator.
Good luck