Only 7k and 10k? Pish, you aren't drowning in food until you have 20k+ of each. I once had a fort where an area roughly the size of that entire room was just food stockpiles. That was too much food. Also yes, precious wood need not be sullied with making barrels and bins. Rock pots and lead bins for everyone!
I personally would never have such huge farms. One 3x3 field for each crop works just fine for my forts, and often gives me overabundance even for 200+ population, so my underground plots are often only the size of that top plot there for all the farm. Skilled planters make a huge difference, as well as fertilizing if you have the wood to spare.
If you don't do all the secondary food/farm industries, I recommend you do. They can help eat through surplus plants quickly. Process pigtails for cloth, dimple cups for dye and get a nice clothing industry running. Mill and process all such plants, and cook everything into nice roasts. When you get swamped with seeds, forbid a select few of each plant from your stocks screen, then make seed biscuits - I often end up with thousands of seeds by year 3 or so, that's a lot of prepared meals and edible food waiting to happen, and you only theoretically ever need one seed of each plant to restart the whole crop.
In terms of layout, it's not my preference, no. I like splitting up my food stockpiles -> One takes "raw" ingredients such as meat, plants, cheese, etc. This stockpile does not accept barrels. The second takes only drink and other processed things like syrup, and it does accept barrels. The kitchens are next to the latter -> this makes them grab the delicious dwarven syrup for dwarven syrup roasts. I also keep a stockpile of only prepared food next to my dining area, and a seed-only stockpile next to the farms. Streamline everything!