Hi adarable and welcome to the fiddlerman.com forums.  I have a *very* similar shaped electric.

And yes, I had trouble finding a shoulder rest to fit it.  Same problems, only a couple music shops that don't carry a lot of violin gear in town.  I tried the ones they had, though, and none of them held it well.

For a while I used a shoulder rest I made from some foam and wood and cloth.  Then I found one that fit my oddly shaped violin, by dumb luck.

The rubber band and foam pad, you can ignore.  My violin came with a different chinrest than yours and the metal clamp digs into my collarbone.  The rubber band and pad are just to pad the clamp, not to hold the shoulder rest on the violin.

I took off my shoulder rest to get a couple pics, so maybe the more experienced folks here can identify it for you, since it would be at least a good bet (but not a sure thing) that if you can find one, it might fit your violin as well. 

I don't know what brand/company HJ stands for.  It came with a cheap acoustic violin I bought.  I didn't need it for the acoustic, so I tried it on the electric, and it works. 

I tried other brands that looked similar at the local music stores and none of those worked.  This one, for some reason, did.  I can turn the violin over so the back is up and hold it up just by the shoulder rest without the rest coming loose, which was the the test the guy at the music shop tried with the other brands that they failed.

Anyway, Hope that helps a bit.  If not, there's a thread on the forum where I took pics while I was making a home-made shoulder rest for it that I used to use before I found this one.

But yes, it is a problem to find a shoulder rest that fits, because the body is shaped different than most other violins and neither yours nor mine has the "rim" along the back edge that a shoulder rest's feet usually hold on to.