Cann't you pass it through a level shifter which operates from 3.6 V?

There is something called Nakagome Charge Pump used in ADC's for the sample and hold switches. This video by Prof. Shanthi Pavan IIT Madras. The clock generated is not 2Vdd to zero, but 2Vdd to Vdd. But given you have 2Vdd voltage, you can drive an inverter using 2Vdd supply. But the catch is that if your inverter is taking huge current, then your Cap sizes will go up. This is just like any other switched capacitor circuit. We can interpret the current pumping capability to the impedance of the source which depends on the frequency of switching and the capacitor.


https://youtu.be/8yo42AFczvo?list=PL2135D8A0F7441AE1&t=1950