I've not got an electric poacher Jackdaw - I use the shaped things that you butter and then put in water.
But I use an electric egg boiler every day and it's brilliant. I wouldn't be without it. Pricking the top is no problem and - once you get the timing right - you're good to go with however you like your eggs.
Have you tried lining a cup with cling film and twisting the top tightly - leaving a bit of room - and dropping into boiling water for the required time?