When I was first looking for a good portable camera, the LX100 was on the top of the list. When looking at research, the LX100 provides great IQ (at 4k) in a good compact device for the price.
If you have not already looked at these sites, I would suggest looking up TheCameraStore review on YouTube, CameraLabs, Dpreview, and EOSHD.
LX100 does also have many limitation.
With a fixed lens system, your focal range is set to certain range. This may not be an issue initially, but can hamper longer term use of the camera.
Having a smaller camera brings up the issue ergonomics and vibrations during handling. In the efforts of compacting the size, there is no flippable screen.
If I remembered correctly, the LX100 has a clicky control ring. This may causes issues when your are trying to focus pull smoothly and cause background audio you will need to clean up.
All the other issues you mentioned about no mic jack and limited picture profiles can be all a concern. (I do believe it has a hotshoe, because it comes with a separate flash unit).
Shallow DOF, while great for a camera this size, will be less than the Rebel with APC sized sensor. With the lack of a tele range for your lens, this will compound the limitations.
My question for you; is 4k needed for your workflow? With the shift of displays going 4k, there is something to be said about future proofing your work. If you are just getting starting in videography, 4k maybe more trouble that its worth. If you want to output 4k content, you will needed a powerful computer for editing, 4k monitor, and good amount of storage.
If you need the 4k (and want the lowest price), LX100 is a great choice. If you have more flexibility in your budget, I would also suggest looking at the Samsung NX1 and the Panasonic GH4.