If you horizontally orient and horizontally align them all in one column, wouldn’t you still have better finger access to all of them by grasping the sides?
Also, I think you misunderstand what I mean by “vertical”. I mean a vertical mount connector rather than a right-angle connector. The link in my last reply should clarify. A “vertical” phoenix style connector would have wires coming out of the screen relative to your image, in the same way that every other joulescope front panel connector works, and the way the JST and 0.100" header connectors on your panel would also work.