I would probably go with a 750w psu for 1070 sli on X99 although you could probably get away with 650w. Take a look at these:-
My basket at Overclockers UK:
The Bitfenix Whisper 750w is a CWT built unit with quad 12v rails. Each group of components has it's own rail so 12v1 is for Motherboard + Peripherals, 12v2 is for CPU, 12v3 is for GPU 1 and 12v4 is for GPU 2. The full 750w is available across the 12v rails and it has a 7 year warranty. Review of the 850w version
here.
The XFX XTR 750w is a Seasonic built unit with a single 12v rail of 744w and has a 5 year warranty. Review
here.
The Superflower Leadex gold has a single 12v rail of 749w and has a 5 year warranty. Review
here. Be aware that all Superflower Leadex models have bright white led's where the cables plug in and they cannot be turned off.
The Superflower Leadex Platinum 750w has a single 12v rail of 749w and has a 5 year warranty. Review
here. Same as above with regards to the led's.
The EVGA Supernova G2 750w is built by Superflower and is basically a Leadex Gold with a different fan, no led's and a longer warranty at 10 years. It has a single 12v rail of 749w. Review
here.
The EVGA Supernova P2 750w is built by Superflower and is basically a Leadex Platinum with a different fan, no led's and a longer warranty at 10 years. It has a single 12v rail of 749w. Review
here.
The Corsair RMx series is argueably the best series that Corsair sell and the 750w version is no exception. It's a CWT built unit with a single 12v rail of the full 750w and has a 10 year warranty. Review
here.
Some of them would have to be used with cable extensions if you wanted braided cables. This is a much cheaper option and would not be a problem with your case as the psu sits in it's own compartment anyway. If you still wanted full cable sets then you are limited to the Corsair RM750X, XFX XTR750, Superflower Leadex Gold and Platinum 750w and the EVGA G2 and P2 750w.
Personally I would always go for braided extension cables, especially with a case such as yours where the psu is hidden away as it's a much cheaper option. These full cable kits range from half to three quarters of the price of the psu.