I just realized that a following hack could be worth trying:

1) we have the main PI with all pins already taken but with an available USB port

2) we connect the cheapest 5$ no-WIFI variant of RasPI Zero to the USB of the "main" PI, and we put the inkyPhat on this pi zero

3) wittyPi starts the main PI

4) power starts to flow to main PI's usb port, hence the small PI starts

5) the main PI can communicate with the zero in a sort of ethernet-emulated through USB, c.f. https://www.thepolyglotdeveloper.com/2016/06/connect-raspberry-pi-zero-usb-cable-ssh ... for example, an image to-be-displayed can be sent from the main PI to the zero

6) once the image is transfered and displayed on the inkyPhat, pi zero can communicate to the main PI that the job was done and halt

7) additionally, the main PI can shut down the USB port through which the zero was powered ... c.f. https://www.raspberrypi.org/forums/viewtopic.php?t=93463 , if  that hub-ctrl.c will work than it is a hammer

8) when a new image is supposed to be displayed on the inkyPHAT, power flow to the USB port can be reactivated and steps 4-7 can be repeated

The idea is to counterbalance the deficit of GPIO pins on a PI with communication with "peripheral" zeros, which have a new full set of GPIOs, are small and cost 5$ a piece...