At this stage, you receive a view object right before it is rendered on the screen. However, this applies to all views, so I needed to specify the specific view/display. Selecting the view was easy-
if ($view->vid == %d) * %d == the required view id
However, I struggled on selecting just the display I wanted to affect. After lots of googling, I found the answer-
if ($view->vid == %d && $view->current_display == %s) * %s == page_1, page_2, block_1, etc
After that, it was a matter of setting-
equal to my form. All done!
Given my initial impression of Views, the object and handlers could really use some simplification. However, I'm sure there's a reason for all of it that I'm just not aware of yet (please feel free to drop some knowledge in the comments).