After a week of after-work evening debugging sessions, adding bypass capacitors at "strategic locations" which had zero impact on the display stability and looking at the signals under a scope, I realized that the issue actually is the "ringing" during the switching of the inductor, so bypass caps addition wasn't really helping us here at all.

The solution was to add a "snubber" consisting of an RC network at the FET switch [SW] terminal of the boost converter to dampen the transients. This TI appnote proved to be helpful: minimizing ringing in boost converters. I took the values straight off the appnote [10R and 330pF] and after soldering them and powering up :

This is just the first step. Next up is to get it working with the capacitive touchscreen, and then put it all in a nice lasercut / 3D printed housing for this thing.