Help...revisiting the speedo cable bounce???

Hi all,
Still trying to piece this 92 hatch back together inside.
The speedo needle had been bouncing real bad at speeds below 30. I pulled the old cable out and replaced the entire thing...sheath and cable. I did the search thing here and got a mixed amount of suggestions on proper lube of the cable. I tried using graphite first. Got it back together and yes, the low speed bounce was gone, but then it was doing a high speed drift...above 40mph the needle would just float around +- 30mph!
Yuck, so I pulled the cable out and cleaned it off, then tried regular all-purpose grease. This time it was smooth as silk...for about a week. Now it's back to bouncy needle. Each time I drive it seems to bounce at a different speed...sometimes around 20, sometimes around 45, etc. At times it's smooth as silk, then after starting out from a stop it starts to bounce/wiggle at whatever speed.
There is a new driven gear that is in excellent shape going into the transmission.
Is there a grease i can use to solve this issue once and for all? I am nearing the point where I put the instrument cluster and housing all back together, so I would like to get this thing done right.
Thanks for helping out again,
Ken

Yeah, I know the 3.73 gears and speedo gears aren't a perfect match. I do, however, know that this particular setup has worked in another mustang just fine...in terms of a steady needle.
What I noticed is after greasing up the cable the last time the needle really worked great for about a week, then slowly started it's bouncing routine. It was like the lube dried up and let the needle start to bounce again...getting worse each week. Since it can go a week being nice and steady at all speeds, it leads me to believe it has the potential to do the job. I'm just hoping I haven't done the lube with the right stuff yet and there is still hope for me!
I did think about the weather temps, but we have been pretty consistent here running in the 80s.
Any other ideas or thoughts?
Thanks,
Ken

Thanks JR.
I don't find any lubricant high up on the cable end, but also don't know the history of the car either. I just find it funny how the cable works great for about a week after being lubed, then starts to get the wiggles after that. I'm going to pull it one last time and take a look.
Thanks for the info,
Ken