I have yet to do the headset on my bike and probably won't for some time since it's completely fine
But I did repack a pedal. I tried Finish Line w/Teflon and it was simply too thick. I tried thinning the grease -many times with varying amounts of each of the following
chainsaw oil- that helped ..Once I squirted in quite a bit of some Pedro lube to the concoction the pedal turned very smoothly -nearly as well as the perfectly greased pedal which I hadn't yet touched ..although, the sound of the pedal revolving wasn't as dampered as the untouched one. Hard to describe the sound created -not a grinding one, though. I then added Crisco to the mix for it's thicker consistency to match the appearance of the untouched pedals grease ..but it didn't do anything for the noise.
I went out and bought red Mobil synthetic grease to try
It looked right except for the color
Too thick. Too much drag like the FL w/ teflon grease only.
I also bought some cheap amber and white lithium grease
I tried the amber one first
barely coating the bearings in the grease before placing in ..CAREFULLY. The grease isn't thick enough to hold the bearings in and too much grease just adds to the drag
Perfect. Still isn't QUITE as smooth as the untouched pedal but it's not noticable to anyone but me. No noise.

I'm thinking a light coating is all that's needed. Too much and stuff just doesn't move as nicely.
The grease isn't the same as what's on the other pedal ..that pedals grease is thick
This lithium turns very liquidy as did all my other experimental grease mixtures ..but none ran out.

For bike purposes don't worry about mixing greases
Ordinary lithium grease is the cheapest I found and works very well. If your headset turns well I'd leave it ..putting in more may make everything appear to be better taken care of
but it may just be a waste that increases drag.