I have been having issues with my stem/headset area "clinking" since right after getting my bike. It didn't do it when I first got it, but right after making some adjustments to the handlebars in which I removed the stem.
Since then I get a tink, tink every pedal stroke from pulling on the handlebars.

The other night I decided to look at it, again...I have taken everything apart, checked for cracks, lubed all the contact surfaces, etc. I found that the noise is actually coming from the top race of the headset, or at least there is where it eminates the loudest. I found that when putting the stem back on that it would not do it, until I tightened the stems pinch bolts a little past finger tight.
So, will leaving them just "barely" tightened be safe? Is this actually the correct way to have them?
The stem doesn't move on the steerer easily or anything, it just doesn't seem to me to be tight enough...although I have found that I was overtightening my seat post too...now that I am on my second carbon post from crushing the original.

It sounds like you aren't setting the headset preload before torquing the pinch bolts.
Use the instructions found at https://www.parktool.com. Torque the pinch bolts to 4 - 5 nm range.