What a very interesting problem to solve.
IF your only talking a few thousand shapes I have a simple solution.
Only have your polygons in the map
Set up data driven pages with your polygons as the layer. Make the outline of your polygons a nice thick layer and maybe even give them random colors for a fill.
When setting up DDP sort by objectID
set up labels for the polygons with objectID right in the middle and big enough to see easily.
Page set up to 8 1/2 by 11 with no margin.
Export the DDP as PDF multiple sheets using a . ( find that tends to work better with large numbers)
use lower resolution and faster output. When they are all created combine the pdf't into a single pdf.
then simply eyeball them. you can use your arrow keys to move from one to the next pdf. when you find one that is shaped like an L or a T then you address that situation.
sounds cumbersome but you should be able to get to the point of browsing the PDF's in very short time, depending on how many polygons your talking. If you lower the resolution and quality and only have the polygons on the map you can generate many thousands of PDF's very quickly.
I have a more complicated mathematical idea in my head but I need to think on that.
