I am also happy with my Nature's Head.
Here's a link to the
installation page which includes a diagram with dimensions:
https://natureshead.net/installation/
Without knowing more about the space around your 10" base it's hard to guess whether it would fit, but the 9" bottom of the solids container might sit well assuming you have clearance behind. The unit is anchored by two L-brackets, one on each side of the solids container, you can see one in the diagram just forward of the spider handle.
The spot where I put mine has a similar dimension to yours, an old
fiberglass base for a
jabsco head. The unit sits firmly with no troubles. You can see the L-brackets that secure the base in the picture. The liquids bottle projects out over the floor of the head compartment, which has a
shower pan with a small sump below the
wood grate. I've had no problem with it sitting suspended, however I put a small step unit under it so I have somewhere to rest my feet rather than having them dangle.