I always experienced them 'back-to-front' as well, and I believe it is what happens if your eyes are focusing on a point in front of the picture ('cross-eyed') instead of a point behind it.
With a lot of effort, I can see it the right way by putting the image very close to my face, and relaxing my eyes to focus on an imaginary point beyond the page/screen. Then I slowly back away so that the image fits more comfortably in my field of view. However, I still find it very hard to bring the image into sharp focus, and at any moment the illusion can suddenly disappear and I have to start again.
I have excellent vision but after trying to look at these stereograms for a few minutes I am suddenly having difficulty focusing on normal objects around me. Quite unnerving.
Is that how you see it so that the object is coming out at you? The way my brain sees it is that the background retreats away from the screen plane so that the object is just at the same level as the screen. More like I could crawl into the world that just opened up through my screen vs catching something coming at me from out of the screen.