I read all the highly laudatory on-line reviews of the 70-300 non-L, and came to realize that all the folks claiming that the lens was of almost L quality had crop sensor bodies. Which if you think about it makes sense, since on those bodies only the middle portion of the image circle is used...the good portion, of course.
I tried one on my 5D3 and while it was nice and reasonably light and easy to handle, I was not overly impressed with the image quality away from the center. So I bought the 70-300L. Which provides spectacular images, but is very heavy and for me almost unpleasant to use. The IS works perfectly, which is good, because it is absolutely essential for me. Although if you are used to the 70-200L with 2x extender, you're probably use to the weight already.
Perhaps if you find that the fence blurs the edges of your images all the time the non-L might be OK for you, as you wouldn't be using the area that is poor nearly as much.
Personally, I find myself using my 24-105L and cropping the photos more than using the longer lens.
If you need a long lens for things like air shows, you will love the 70-300L, and the price is right at your target point. As others have recommended, you can then sell the 70-200 and 2x and buy a 24-105L. You may be surprised at how much use you get out of that lens vs. the longer one.
I hope that was at least slightly useful...