It is so easy to get people to help spend your money on this site, sometimes wonder if we are guilty of supporting equipment addictions.

Just to back things up a bit, were you planning on keeping the 7D and the 17-55 when you upgrade? Would be a more compact setup to carry around at times. Also, if you do wildlife the pixel density on that crop sensor is not easy to match (same pixel size on FF sensor would be over 46 MP). The ISO range and noise levels won't come close to the 5Diii but the extra pixels on target do allow major cropping. Depends on your intended usage of course.

If you were planning on selling them off I'd suggest waiting to see the test results from the hopefully coming soon 24-70 II. Paired with the 70-200 this would be the start of an amazing lens collection

70-200 f2.8 ii is an amazing lens. Use it very often for sports and events. Doesn't have the reach of the 70-300 but the aperture and the IQ have made it indispensable to me. I find the 1.4x TC to work very well with it. The 2x TC III I am not as convinced of. For filling the frame with close objects I like the results. For intense cropping or distant objects I am not a fan. Other people have no issue with the results. Highly subjective and I am quite fussy about the in camera results as I would prefer to shoot pictures rather than spend time processing images. Also when shooting on contract the images delivered are JPEGs straight from the camera with no processing. Might be part of why I am so particular about these things.

Should you replace the 70-300 with it? Depends on how often you use the 200-300 mm range and whether you are happy with the tradeoffs between cost, weight, aperture, and IQ. Do keep in mind that the sensor crop factor of the 7D will be VERY noticeable when you go FF. The 100-400 may be another lens worth your consideration, though you probably already decided in favour of the 70-300.

Any of the other lenses already mentioned by others would also serve you well, if the lens is a good fit with your typical usage. The 100 mm L macro lens is one that is easy to recommend because it is so versatile with the IS system in it and macro capabilities opens up whole new areas for you to explore.