"Might also be better for them to not get extra Body Parts at the start, and instead only gain them through extra starting Mutations, just to keep things more consistent."Yeah, this sounds like the easiest way to remedy the issue. I know that some players are particularly interested in having a random assortment of limbs, but to be able to allow for that, while also keeping stats consistent, would be more difficult. Having extra limbs through mutations would make more sense to me. For now, at least.
"...I wonder what happens if you've got the Wings Mutation, and an enemy cuts off the wings, do you still retain the speed buff[?]"
Yes, technically. But having a wing severed would reduce your movement speed by the amount dictated by the body part removed. I have a feeling having both wings severed would reduce your speed by more than the mutation's bonus would give you. You can use the console if you'd like to make specific "science-y" checks.
Alltogether, it seems like I need to put some more thought into the body part system, specifically how body parts interact with your stats. If it doesn't make sense to the player, then the system is flawed.