I went the same way (7D to 5D III) and what a jump it was. My 2-cents worth:
I have the 16-35 and love it but as most said the 17-40 for 1/2 the price will work too but I don't think it's as good as the 16-35. If I had to do it all over again I would still choose the 16-35 because it is a great lens indoors and much faster than the 17-40. I love to shoot landscapes and either one is great for that.
I prefer the 24-70 over the 24-105. Again I like the faster lens and when I tested the two side by side on a tripod the 24-70 was much sharper/cleaner throughout the entire range. I thought the pics from the 24-105 were kind of flat looking and when the lighting became poor/questionable the lens didn't perform well. I will say the 24-70 I have is a very sharp copy. It has been sent to Canon and was calibrated to my 5D III.
The 70-200 MkII is a no-brainer. All I can say when I use this lens is WOW!
Now to the main reason for my post. I notice you used a 70-300 with your 7D. Did you shoot a lot at 300mm? Biggest thing I found going from the 7D to the 5D III was how much closer everything was to me when using the same lens because of the loss of the crop (1.6) factor. Had the same issue with how wide the field of view became too. I planned on selling the 100-400 when I picked up the 5D III because I didn't use it much with my 7D but now I find I am using it all the time. Looking at your 300mm it's actually 480mm on the 7D. If you like to go long you might need to look at a 400mm+ for the 5D III. The 70-200 will be way short if you liked to shoot 300mm on the 7D.
If I only had a choice of two lenses because of budget I would take the 24-70 & 70-200. Can't go wrong with this combination and it should be able to cover most of what you want to do. Primes are great but if you hate foot zooming like me and want to minimize your costs I think these two lenses are the best choice. Good luck with whatever you do. The 5D III and going FF was the best choice I ever made. I don't miss my 7D at all.