This might be too late, but could you consider embedding/soldering the SSD chip onto the mainboard?
Samsung released BGA SSD last year, the PM971, followed by Toshiba a few months later with the BG series SSDs. If my approximation is correct, this would buy us around 4 Wh of battery, basically giving us 52 Wh battery or roughly 50 minutes of battery life. If its too late, at least this would be useful for the second-generation V next year
Here's the size comparison
One device I know that uses this kind of SSD is the MacBook 12", they were able to basically fit the entire computer in a board as big as a Raspberry Pi, although with no upgradeability whatsoever.
I am right now using the SM951 (similar to 950 Pro) on my desktop PC. While the speed is impressive, I read from the reviews that the power consumption isn't that great.
One that impressed me is this Sandisk Z400s, where its tested to get better efficiency than the 850 EVO. Apparently the key here is to get a DRAM-less and cache-less SSD. The good news is the pricing is on the lower side, and it seems to be made for OEMs in mind. The bad news is its not PCIe / NVMe, but I stand by the original consensus that NVMe doesn't provide any significant advantage on this type of devices.
Based on the testing done by TomsHardware, the Z400s is able to get 668 minutes, while the 850 EVO can only manage 621 minutes.
TomsHardware states that they use the Lenovo T440 with 6-cell battery for SATA SSD reviews, which has 47 Wh capacity. (source: http://www.tomshardware.com/reviews/how-we-test-storage,4058.html#p11, http://shop.lenovo.com/us/en/laptops/thinkpad/t-series/t440/#tab-techspecs)_
That means, the average power consumption with the Z400s would be:
47 Wh / 668 minutes = 4.22 W
And the average with the 850 EVO:
47 Wh / 621 minutes = 4.54 W
That's a delta of 0.32 W
If we subtract that to the 4.364W that we got earlier, that would give us:
4.364W - 0.32 W = 4.044 W
That leads to a battery runtime on the Eve V of:
48 Wh / 4.044 W = 11 minutes and 52 minutes.
That is almost an hour difference, which would theoretically increase the claimed battery life from 10-12 hours to 11-13 hours.
tldr: Theoretically, the SanDisk Z400s would let the V get about an hour longer battery life over the 850 EVO, or almost 2 hours over the 600p