mihomes, is there no way to brand the EMD? For example, if your website is BlueWidgets.com, you start calling yourself that, BlueWidgets.com. Tons of companies do it to great effect.
Also, I'm having (and always have had) a tough time discussing widgets that are colored blue, because it's not tangible enough of a thing for me. So I'll use "Affordable Widgets," and pretend that a widget is some kind of tool, like a screwdriver or a wrench.
So you have a domain called affordablewidgets.com. This seems EMD enough for me, because someone might search for "affordable widgets."
I think you could get away with EM anchor linking this, if you do it right. So, imagine there's an article discussing your business.
"'A good widget is important for every DIY job,' said mihomes, owner of [[Affordable Widgets]].'"
That's a great link, because the context it's in and use of capitalization clearly suggests it's a business name. Now compare to:
"Buying [[affordable widgets]] is a cheap way to perform for every DIY job, without burning a hole in your pocket for an expensive tool you won't need forever."
That's a so-so usage. Still decent, but getting to the grayer side of things, perhaps. At least the sentence is discussing cheap tools.
The worst usage I could think of quickly is:
"When you're out and about doing your spring tool shopping, don't forget to pick up some [[affordable widgets]]."
Here there is absolutely no context about why that particular anchor text was used. Okay, it's a sentence about tools, but linking to a site called Affordable Widgets? I can understand why Google might get cranky at that.
That said, you're never only going to use that anchor text whenever you link to your site, or someone else does. Perhaps one of the links from the above example is, "an article explaining why [[cheaper widgets are a better value than more expensive ones]].
I think using an EMD is possible. You just need to be creative with your anchor text and use variation.