I stand corrected. I hadn't realized that lenses that produce razor sharp images were no longer considered magnificent. My apologies.
Also, in my universe... the 70-300mm is very mushy at 300mm. Much mushier then the 70-200mm +1.4x and cropped to make up for the 20mm loss in optical focal length. And while I agree that the 70-200 + 2.0x is mushy (I don't own a 2.0x TC because i don't have an appetite for the soft images) at least the OP would have AF and another 100mm then the already mushy 70-300 "L" at 300mm.
Interesting. I've used a 70-200mm MkI on a couple of occasions, and 'razor sharp' was not my experience, at least when shooting wide open. My MkII, OTOH, is razor sharp.
As for the 70-300L, do you own one? If so, you might want to have Canon check it over - as I linked above (here it is again), Bryan at TDP found just the opposite, and nothing mushy about the 70-300L at 300mm. Now, if you want 'mushy' just set that aperture drop down to wide open (f/4) at 280mm - like this.
There is certainly a lot of copy variability among lenses. I do not own a 70-300L, but i was very interested so I did my due diligence to try it out. I found that it was quite nice through 200 but at 300mm really dropped off. As for the 70-200 F2.8 Version I... razor sharp.
And my benchmark for sharpness is my 300mm f2.8 IS version I.
I will repeat though that copy variability can be a source of opinion both good and bad for lenses. Take the 100-400 L lens as a prime example.....