We used one of those at the zoo that I volunteered at. Can't remember how well it worked but I do remember someone on here saying that is how they do it.
Anyways, I researched this like crazy as I really hate to peel away half the egg I'm trying to eat.
It simple really... Hot start, cold finish. Doesn't matter if your eggs are fridge or room temp. Salt in the water doesn't change things.
Get your water boiling, drop your eggs in. When cooked to desired doneness, shock with cold water. I use running tap water because it's cold from our well. Some people will use an ice bath. With this method I get about 90% easy peel even on fresh eggs which are much harder to peel than old eggs, as I'm guessing you've figured out.
This method REALLY works. I'm not passing on hear say but my actual experience.
That being said, a steamer with a timer you can set and forget might be nice!

But I also don't like having single use appliances in my kitchen. Space is at a premium. And most other things get steamed on the stove top or in the microwave.