When reimplementing Drupal.tableDrag.prototype.dropRow(), how do I access classes of would-be parent?
Get a reference to some parent DOM element ... the jquery parents() or parent function(s) comes to mind. Then use hasClass on those parents as needed.

some parent would be something like the following based on your example:

var parents = $(self.rowObject.element).parents(/* a selector to limit the type of parent, td, tr, whatever */);


EDIT:

dragged rows get a class of like .dragged-previous. The file tabledrag.js doesnt care about the current row, nor about IDs of anything during drag -- its just doing a DOM swap of rows and inserting the dragged row before another row; and assigning a Drupal weight to the hidden weight column. So cant you use like jquery prev() function to get the immediate previous element:

var parent = $('#menu-overview tr.drag-previous').prev();


I'm taking these values from a Main Menu tabledrag example of a vanilla D7 site: