Dave:
If we take the same example of a 45° slope with 15' max on the horizontal, that would be 21' on the slope. I don't think that could ever be allowed.
Again, I have always done 6' on center minimum on the slope as that is how I was taught that NFPA 13 req'd. I can see the argument for the 6' being measured horizontally, and will likely start applying that to my work. However, I think the max still must be measured on the slope no matter what the slope is. You may run into an issue with something like a 67° slope where 15' on the slope is <6' on the horizontal. However, I can't say I have come across something with a slope to that extent.
This has been an interesting thread.
Travis Mack
MFP Design, LLC