QUESTION: Do you think I should get the T4i/T5i (with video autofocus), the T3i (without video autofocus), or something else?

ANSWER:
Whenever I am going to make a tech purchase, I always try to figure out exactly how I envision myself using the product. This makes it very easy to then decide what features are going to be essential. For example: If I was going to be mainly using the camera I purchased for night time videography, I would want to get a camera that can shoot at a high ISO, a lens that has a wide aperture (to let in more light), and one that has a big sensor.

In your case, the question you want to be asking yourself is: "Am I going to frequently be filming in situations where autofocus would be extremely helpful?". These would include vlogging, sports, filming yourself (because you couldn't be controlling the focus), and many other situations. Since I don't know what you are going to be using it for, this is really up to you to decide. Having autofocus, even if you don't use it much, is always a nice option. That said, the cheaper price of the T3i is appealing (especially since it means that it leaves you more money to spend on higher quality lenses, tripods, lights, etc.)

T4i & T4i side by side.

If you think you are going to need autofocus (and don't really need the picture taking ability of a DSLR), I would look into getting a camcorder. They offer better in-camera stabilization, far more responsive autofocus, and can usually be bought for cheaper than the T4i.