I would guess your suspicions of over-watering and inadequate light are incorrect. These are outdoor plants, so growing indoors is going to be a struggle, albeit in the winter it will be necessary because Echeverias are not hardy. If temperatures are warm, it's usually imperative to get the plant outside and gradually into sun (gradually, or else the leaves will sunburn due to being moved from shade abruptly into direct sun). Low light will have the plant stretching, as you're seeing. Be sure your soil mix is extremely well-draining; soil the plants come in from a store and any bagged soil isn't going to cut it. You'll want to water when the soil is entirely dry, so when in doubt don't water. The over-watering and poor soil is what'll get you those mushy, fallen leaves, in my experience, and you just have to do your best to get the plant through the winter, while watering little, until spring and warmer temperatures.

It's leaning toward the brightest light it can sense. If you turn the pot a bit every few days, new growth will be more upright.

Perfection is nice -- but a bit of a lean gives it character, no? And you won't notice the lean so much when the lower branches grow larger.

Thank you so much to the both of you for the help! And yes, I suppose it does add some uniqueness!

How would you properly determine the moisture of the soil? I find that when I feel the surface of the soil, it is not very accurate. I'm currently using a cactus mix I bought from the store.

Not sure but it looks like an Echeveria imbricata or something similar. As said it is not winter hardy but it needs significant sunlight to grow properly; yours appears etiolated, stretched out. As for watering, only you will be the judge of that as only you can determine your humidity, temperature, etc. When the top ý" or so of the soil is dry, water. In spring, remove the top portion and you'll make more plants and the remaining stalk will grow new heads.

When you water, I'd take the inner pot out of the cache pot, so any excess can drip away. I usually pick plants up to see if they feel light-as-air yet (compared to the heft of when it's just been watered.) When they do, they're dry.

Your pics: