Making a list of the row title under the corresponding column title in if a cell has X

Sorry for the confusing title, I couldn't think of a concise way to summarize what I want to do. I want to have an input table with the column titles being the title of something and the row names as the names of people. The idea is, when the cell contains something, probably an X, a separate table with the same column titles will populate a list of the names X'ed in the corresponding column. Below I have attempted to make some tables with what I imagine it looking like.

Input table where cells are X'ed as needed.

	1000.1A	2000.2B	3000.3C
Smith			X
Jones		X	X
Williams	X	X	X

Output table where the list is generated based on the X's

1000.1A	2000.2B	3000.3C
Williams	Jones	Jones
	Williams	Smith
		Williams

I am able to get the names as an output to the correct column, but I do not know how to move them up to the top-most open space. Right now I am using =IF(B2<>"",A1,"") to get the name in the appropriate list. But as you can see, it will leave an empty space for that row under the output column. This is where I get stuck trying to squish it up to the top.

Also, as a separate note, I would like to sort them by alphabetical order when they are in that column.

Any help is much appreciated.