First off... what a fantastic photograph! I am a huge fan of it.
Now please allow me to be upfront with you on my perception regarding your answers to my questions... I percieve that your view of this photograph is more of an emotional one with your attachment to the dogs that are in it? I think perhaps that is why you wish to focus on them?
I would therefore appeciate for you to step back for a moment and take an objective view, and see the image from a 'different' perspective... as a general observer of an artwork.
I believe that the dogs are not the focus of this photograph. Consider how their backs are facing towards us; and consider how unsharp they appear in the image. To me, the most interesting aspects of this image are the tree branches and the vanishing point, as shown with the two yellow circles in the image below:
I believe that by trying to make the dogs the focal point, you are taking away from the most interesting parts of the image; and this is perhaps why you are not liking the crop that you presented earlier. Let me try to explain some more with this image below:
See how the dark tree trunks, on either side, frame the image? ...especially framing the tree branches in the above middle?
And look at the beautiful leading-lines below, drawing the eye to a vanishing point.
So, I personally don't think that your photograph needs much cropping, but I played around with a few crops keeping in mind your preferences and reasoning; and here is what I came up with:
I cropped off the sunbeam going off on the left; and I cropped off some of the road (mostly from below); I positioned the vertical middle onto the thicker tree trunk; I also used two of the leading-lines, starting them off from each of the bottom corners.
However, if you wish to present your photograph as an artwork to the general public, and not as a personal portrait of the dogs, then I recommend that you make a crop that encompasses the image as a whole.
And if the sunbeam, going off on the left, still is not to your preference, then perhaps consider editing the image to tone down the strengh of that sunbeam? Something like this, as shown in the next image, which is also my personal preference to cropping your photograph:
At the end of the day, the photograph belongs to you, and you must edit it as suits you best. I am just one of the many many beholders. Thank you for sharing your beautiful picture with us.