I haven't tried the WFT-E6B for the 1DX, so I don't know the answer to your question.
But apart from that, let's assume you get 90 minutes out of a battery, which then takes 120 minutes to recharge.
That means you'd get 180 minutes out of two batteries. Meanwhile, the first has recharged for 90 minutes, and ought to give you another 60 minutes of operation. During that time, the second one has recharged for 60 minutes, and would then run another 45 minutes.
This is continuous operation for 4 hours and 45 minutes. Wouldn't it be time for a lunch break then, a break during which you have both batteries in the charger. That would allow the one that started recharging first to complete, and the second one to also complete, before you've run out of the first, when you resume shooing after lunch.
This is perhaps not an ideal way of working, but to me seems fair enough so you can evaluate if you really need to buy another battery just for this purpose.
Since you use the WFT-E6A, not the built-in Ethernet, I presume you don't want any wires connected to the camera? Otherwise there's a power kit which allows you to run the camera from a wall socket, but that does of course imply another cable.