The reason it is building up on the lid is because the temp in the tub is at times greater than the temp outside the tub.
If your herpstat probe in also inside the tub, try putting it outside the tub. It will keep a more stable temp inside your egg box.
Having the probe inside the tub is not the most efficient way to control temps because the air outside is going to get up to temp alot faster and will exceed maximum temps needed to heat the box.
Consequently when you achieve the desired temps inside the egg box the air outside will rapidly cool because the herpstat thinks that it can adjust to a much lower temp. It will take more time for the temp in the egg box to come down and by the time it does the outside temps will be much lower than you want. Which is the most likely reason the condensation is building up inside the box.
All you have to do then is place a probe that monitors temps inside the egg box so you can see that it is definitely heated properly. But you really won't need to monitor that temp at all. It will always be within a degree or 2 of the outside temp. Which is more than adequate for incubation.
Try it out.
-Steven