You should be able to get a good soft boil by plopping the lid on and letting the steam do the work.
In fact, I don't boil eggs, I steam them. I use one of my Fissler pressure pots (2.4L, I believe), add a cup of water and puncture the air sac end of the egg. Once it comes to pressure, timing is easy and the results are very consistent.
Here's the best part. The pressure seems to separate the egg from the membrane inside the shell, and the boiled egg literally slips out of the shell.
Half of what we read or hear about finishing is right. We just don’t know which half! — Bob Flexner