How to find a suspension noise when nothing is loose or broken?

The Mustang world has had noise issues with camber caster lates making noises also.

FWIW

My first thought was sway bar links because they can make an incredible amount of noise when they get worn well before any handling effects are noticeable, but camber plates are a likely culprit as well, they can also make a ton of noise if anything is loose or worn. I remember one time my AE92 had a slightly loose top nut on a camber plate and it sounded like I was driving a silverware drawer.

So I believe woody said it already.  I know the PO also said motor mounts were replaced...

I had this same issue on my silverado.  It was motor mounts.

Doesn't hurt to double check!

How are the subframe bushings and mounts? 

Play in the subframe could cause noise while the front end is tight. If you are lifting with a jack or jackstand under the subframe, then the bushings will be loaded and there won't be any play  

Are any of the mounts or bushings that were replaced a round press in style? If installed in the wrong orientation they may allow too much movement and bottom out causing clunking. 

There are no front subframe bushings, it only has control arm bushings and the rest is all solid metal in the front.  Motor mounts are new factory ones that have less than 10k miles, I will check again this weekend to make sure they are tight though.  It's definitely not the swaybar endlinks, I took the swaybar completely off and put it back on with brand new endinks and that didn't change anything.  I took the camber plates off a while ago and that didn't help either.