Figured I would keep relevant noisy belt / pulley issues in this thread.
Trying to diagnose a slight chirp in my engine bay.
Mine was the fan pulley bearing.
Mine started with a cold morning chirp like you mentioned, but then turned into a bad bearing sound (gargling marbles) after about a month. Fan felt firm with the belt on, but with it off, it had about 1/8" of play. I couldn't reproduce the noise by hand, but figured since there was play in the fan, and it would spin and catch like you mentioned yours is doing, and every other pulley spun free and smooth, I would replace the fan pulley bracket. Fixed it.
A lot needs to comes off to get to it, but it's not hard.
If this ends up being your issue, I would definitely go with an OEM part for this. I've heard aftermarket bolt holes don't line up. Plus the original one lasted a long time. There are a lot of writeups on how to do it here on Mud. Best of luck!!