For some reason it is now working, even though all I did was try the exact same thing again.
I just downloaded the latest Faithful 32x32 version, which is for 1.6. However, when I place the .zip file in the Resource Packs folder and go back to the menu, it does not appear. The only two options I have are the default 16x16 pack and Jolicraft, a 16x16 texture pack for 1.5.2 that I ran through the conversion tool myself. I closed both Minecraft and the launcher to ensure that this wasn't just a matter of Minecraft not having been told to check for a new pack in the folder, and it still does not see it.
I'm reluctant to try to run the 1.5.2 version of Faithful 32x32 through the conversion tool, as I've heard from numerous sources that the tool is insufficient for all the features offered by HD texture packs despite recent efforts to natively support them.
This is not a problem with Faithful 32x32 specifically or even HD resource packs in general. I currently have two other resource packs aside from Faithful designed for version 1.6 in the folder, both of which are 16x16. However, none of the three are showing up in the menu.
I am running Minecraft on Windows 7 64-bit with Java 7 update 25.