Keep the 70-200: better IQ and versatility. You could always add the 1.4x later to get close at 280 f/5.6.
I had thought about doing that. Will autofocus still work?
Like others have already stated, AF will work with a 1.4x. The pictures will get a little softer at 100% but is barely noticeable, but it should do well compared to your non-L 70-300. TCs should only be used when you need the extra reach. Losing a stop over the whole range is significant, but at 300, it would be the same/better than your current non-L 70-300 at 300 (both at max aperture of f/5.6).