What do I need to do to use my current recipe for thin-crust pizza?
Tl;Dr Yes, let it rest

It is going to be difficult to give you a perfectly canonical answer to this question because, as moscafj commented, there is a lot of variation in pizza recipes.

Dough Recipes  

Thin crust pizza dough, such as the popular Neapolitan style, is typically made with high protein dough. Your recipe, before your modifications, called for 100% bread flour and would definitely fall in this category. If there isn't enough protein thin crusts will not have the structure to stay together when sliced.

Thick crust dough can get away with a little less protein because they have more space for structure. The less protein the more the crust will be bready instead of chewy.

There are, of course, many other variables that make the difference between thin and thick, for example; thin crusts are often baked at higher temps. In general a good pizza dough recipe can be used for either. 

Your recipe, including your modifications, is very similar to the recipe I use and I have had good success with both thin and thicker (I never go thicker than .5") pizzas.

Getting it thin

With all bread dough- especially high protein doughs- as you work the dough the gluten gets very tight. All bread recipes have resting periods for the dough to relax before it is shaped.

If you are using that much bread flour, you should be able to get your dough so thin that light will shine through.  

If you can't get there because the dough isn't smooth and just comes apart then you don't have good gluten development.
See one of the many questions here on that subject.  

If you can't because the dough is too stiff then you might be working in too much flour and you should learn to work with wetter dough.

If you can't because the proteins are too tight and snap back then let the dough rest a little longer.