i dunno, its hard to tell but the screen header pads look kinda rough to me. at this point after multiple reheatings and ripping the header out, there may well be some that are lifted. you could check continuity between the pads and the main header by referring to the layout, it will be a bit tedious. (if anyone does go through this exercise it would be nice to document the pin correspondence in a simple table form.)
and yes, it’s entirely possible to damage the OLED or its driver chip with excessive application of heat. you want to heat each leg for no more than 1-2seconds when soldering the screen header, given that it is unavoidably attached to the sensitive bits. it follows that you need to be both judicious and attentive in cleaning and tinning the tip as you go.