After seeing posts saying someone fried an AWS F1 board with 300A, and that now there is a 150W limit but it is only a warning, I did a little searching and found that it appears AWS F1 limits your core power (Vccint) to 85W, which would be 100A at 0.85V.  They say they may/will shut you down (gate your clocks) if you exceed this, see https://github.com/aws/aws-fpga/blob/master/hdk/docs/afi_power.md

Also, someone suggested that since the power supplies are current limited, you could just raise the voltage to lower the current, unfortunately this is not how these chips work.  They basically take the same amount of current to do a given job, regardless of voltage.  So the lower the voltage, the lower the power.  This is why chip makers keep trying to run at lower and lower voltages, since it saves power.  

There is another power consideration in all these latest generation chips as well, which is static power (as opposed to dynamic), which is due to leakage in the transistors.  While dynamic power is linear with voltage, static power (leakage) is non-linear, going up as the square of voltage.  It also increases dramatically with temperature.  Static power in general has nothing to do with how much work is being done, hence the name "static".

Note that raising voltage may make you be able to run faster, but faster means yet more power, since dynamic power is highly dependent on clock rate.  You can run certain VU9Ps at 0.72V instead of 0.85V and this will certainly lower your power BUT it also kills your performance by 20-30%.  You can also run certain VU9Ps at 0.9V and get higher performance, with the associated higher power.  Of course the chip vendors charge a premium for these special devices over the standard ones.

So, determining the optimal combination of FPGA size, core voltage, and clock rate is not such a simple task.  As mentioned, we are working with the OP on this.