The "meat problem" (which isn't a problem at all, really) can be dealt with in two ways: keep your animal population low, or keep your cooking facilities well-prepared. The extra meat types are well worth the hassle, however, especially for large animals. A single elephant can now feed a fortress of 200 for half a year. Keep your breeding stocks small and your kitchens well-run, and you'll be rolling in prepared meals before long.
Well, I already produce way more prepared meals, with 3 cooks, than my dwarves can eat, and more than enough to buy out any caravan, by processing my quarry bush leaves, syrup and flours into meals. Those are worth many times more than elephant roasts. And no, I don't want more cooks. There are more useful jobs to spend dwarves on, like smelting, and magma-trap testing.
In my opinion, this many meat byproducts kinda disrupt the balance. I like to cook my dwarves varied meals, and used to be able to do so without accessing the kitchen screen all the time, to forbid and allow ingredients.
I do indeed solve it for now, by keeping my animal population low (caging them so they don't breed), and almost never butchering animals.
What adds to my frustration, is the fact that when processing fat into tallow, instead of turning a stack of 5 fat into a stack of 5 tallow, it now needs 5 seperate jobs, turning a stack of 5 fat into 5 stacks of 1 tallow. Especially annoying with larger animals, where the stack of fat will clutter up the kitchen, making jobs go *real* slow.