3 way Crossfire/SLI is really inefficient as it's quite a lot to spend without the performance to back it up, not to mention the reasonably high end PSU and motherboard you need just to get it to turn on.
A standard R9 270 only requires a single 6pin PCIe, but that card you mentioned uses two, which implies it uses more power. It has a tdp of nearer to the 270X, so that seems like a better card to base judgement from. 750W would be enough, but like you have discovered most 750W are wired for 4 8pin PCIe power (equivalent to 8 6pin) as running multiple low level cards is very uncommon.
The RM850 will do the job, as it does have 6, but I'd give some thought as to the viability of your overall solution.