What you lack in range with the 5D you can make up with a crop as the 5D is full frame. The 5D also has much better ISO performance than the 7D, 6400 on a 5DMKIII is comparable to 1600 so lots of scope there. Difference between 6-8fps negligible and not worth worrying about, the 5Ds AF system will more than make up for it.
I would try a 1.4x extender, cheapest option. If not the 300 F4 IS is a good choice.
Which version of the 70-200mm do you have the MKI, the MKI with IS or the MKII?
The MKII still yields incredible results with the 1.4x extender.