Congratulations on successfully installing the Eaton style posi in your third-gen Firebird. It's a fantastic upgrade, providing a great performance boost. And I totally understand your concern. While it's not uncommon to experience some initial noise or drag after installation, we definitely want to get to the bottom of it.
There could indeed be a connection between the noise and the choice of your friction modifier. Some differentials are quite picky about what you put in them, and not all friction modifiers behave the same in all types of posi units. Hence, it might be beneficial to try a different type.
You mentioned considering Castrol LS 80w90, which is indeed a good choice. Castrol is known for producing reliable lubricants, and the LS 80w90 has been tested in a wide range of applications with positive feedback. Moreover, it's worth mentioning that many aftermarket posi units are actually shipped with Eaton's own friction modifier. So, if you continue to experience problems, you might also consider trying Eaton's product to see if it makes a difference.
You mentioned that you've broken the differential in by idling with the wheels off the ground, which is indeed a good practice, as it allows the gears to mesh and distribute the lubricant without any load. However, did you give it a good drive after the initial break-in? Usually, it's advised to drive about 15-20 miles, while avoiding hard acceleration and tight turns during this time. This can help ensure the gears have meshed properly and the differential has a chance to settle into its new environment.
If you've done all of this and the differential continues to moan or drag, it may be worth taking a second look at the installation. It might seem tedious, but it could be something as simple as a slightly misaligned gear that's causing the noise.
Lastly, remember that these things can take a bit of time to smooth out as everything seats and wears in together. So, give it some time and see if it settles in. If it doesn't, keep troubleshooting with the advice above.
Keep us posted on your progress. The community here is always ready to assist. We're all learning together!
Good luck and happy drivin