I figured out the orientation by comparing the old and new cables - the "top" has the line of gold connectors and the "bottom" has a could of long horizontal metal lines, so basically the "pins" face up.
I swapped the old LVDS cable back in and still had a blue screen with lines, but it mostly went away when I adjusted the screen angle and pressed on the display ribbon cables on the bottom of the panel. Still one vertical line so I must have damaged it during disassembly, but the display works otherwise.