New leaves have begun to grow everywhere, and I mean everywhere. Many of them are growing in sideways or upside down. I realize this is only a cosmetic issue probably, but their strange positioning is making an otherwise very tame plant look kind of....wacky, and making it difficult for them to push their way past the already existing, mature leaves. Is this normal? If so, is it possible to correct? Will they right themselves? Any feedback is greatly appreciated! :)

To me, it sounds like your violet is growing multi crowns, which is normal for many violets.
These can either be removed by un potting the plant, and by the use of a xacto knife, or any good sharp knife, cutting out these little plantlets. They can also be pinched out as well, but by cutting them out, and potting them up, you will be expanding your collection.

By removing these little plantlets, your violet will not only flower better, the plant will keep a better shape.

I'm actually having the same problem as well. I have a violet that I saved from the deadpile at Lowes. As you can see from the pictures below, the plant definitely has multiple crowns. I'm going to seperate them soon, but I see a blossom. So, I am going to wait to see what the blossom looks like before trying to split it. (I'm a noob and it's still hard for me to recognize a sucker from the growth of a new leaf."

Is any leaf NOT growing directly from the crown of the plant essentially the beginning of a sucker? Because if that's the case, I'll catch them before they get out of control.