I would suggest that you are better off sticking to the 7D with the 100-400 rather than shooting with the FF + 100-400 + 1.4TC.
I tried this combo and it worked reasonably in good light. That said, if you are looking for pixel level sharpness, forget it. Also, if you are shooting birds in the trees, you lose AF, hit a max aperture of f/8 and in dark foliage, are at ever increasing ISOs to render the images unusable.
Personally, I would prefer to use the extenders only with a f/2.8 or a f/4 lens.
I never used the 1.4 with the 100-400, in fact I never used the 1. with the 7D much. It just never worked much for me.
I do use the 100-400 with the 5D3 and find it better than with the 7D. I certainly don't miss the "crop factor", its so much better I get more detail anyway. I also use that lens with the 1Dx and while its not top quality its a great versatile lens.
So the question is if I'm satisfied with 400 mm on full frame - I think I'll manage. Strangely I've been moving more toward 'wide angle' in the past year, even in the tele side of things - I like to get a little more in the frame
As far as relative sharpness goes, I do expect the 100-400 to give better results on full frame, especially since I usually shoot at a resolution of around 10 megapixels on average (using mraw). This does mean that if I need the extra reach it is probably better to shoot in full raw and crop in post. I guess I can live with that...
5D3, 5D2, Sony α6000, G16 | SY14 f/2.8, Ʃ20 f/1.8, 24 f/2.8, 35 f/2, Ʃ35 f/1.4A, 50 f/1.8 I, Ʃ50 f/1.4 EX, 100L Macro, 17-40L, 24-105L, 70-200 f/2.8L IS II, 1.4x II, 2.0x III, 70-300L | E-mount: SY12 f/2, 30 f/2.8 EX DN, 16-70 ZA OSS, 55-210 OSS, Metabones SB | FT-QL, AE-1P | FD(n) & FL lenses