Use whatever you want. 1,000mm with a full frame sensor is going to frame it up with lots of room to spare because the corona and the plumes extend out rather far, you will want several degrees FOV for all of it with a little room to spare, which a 6D + 1000mm will do with lots of room to spare. But you'll need tracking to really make this work well. If you're not using tracking, then you will want to use a wider FOV, so in that case, use the Sigma.
You will not have issues with heat with an appropriate filter. You're imaging in white light and it will be a totally void surface, so there's no special image quality to worry about at this scale. You will not be at a scale to see convection cells. You will just see a disc. So don't worry about using your SCT or not, it's fine. Worry about getting a good FOV depending on your ability to track and how you're going to image.
Personally I'd use the smallest simplest setup with the fastest control so that you can enjoy the eclipse and not fuss with equipment. I use tracking though, so I can image at high resolution scales. It's much, much easier to do this at low resolution scale, and I recommend a lower scale for simplicity. If you don't have a tracker, you will need to keep it really wide and be ok with a small low resolution scale.