One way to avoid a temperature drop is to use a container with more water. If you have three litres of water or so for your eggs (more is better), adding the eggs won't significantly affect the water temperature because water has high heat capacity. (In plain language, that means that water won't heat up or cool down easily, because it takes a lot of energy to change the temperature either way.)
So, use lots of water, drop your eggs in when the water is at the temperature you want, and start the timer. If you find that your eggs are are a little too firm or too runny that way, just take note of it and, next time, try for the same amount of time at one degree Celsius lower or higher. Or, alternatively, shorten or extend the time by two minutes.
You'll quickly home in on how to cook your perfect egg that way.