First off, you're going to get overheating if you open the system and don't bleed the air out.
Second, if the engine bay was moist with coolant, you have a leak. It is probably somewhere at the front of the engine. Until you find and fix it, you're going to have problems. That leak is letting air in and that it causing the overheating.
Don't get hung up on how the temperature gauge suddenly climbs to "H", and can quickly go back to the middle. It's a function of how the electronics work. Normally, the temperature gauge reads out the coolant temperature. I suspect that the coolant is staying at about the right temperature. When you get a big air bubble in the coolant, It's ability to cool the engine where the bubble is goes away. The LS has head temperature sensors. When one of those goes over the safe temperature, the PCM commands the temperature gauge to stop reading coolant temperature and to instead read "H." If you shut the engine down and let it cool a minute (or less), this condition resets and if the head temperature is even one degree below maximum, the temperature gauge will go back to normal.
If you plugged in a good scan tool and set it for real time read outs of coolant temperature and of head temperature, you would see what I mean.
Also, there is no way that I have ever been able to tell if a degas bottle is good or cracked all the way through while it is still in the car. You have to remove it to get a good look at it.