The mottled were seen along with the black and auburn back in the hey days. Then all but the black pretty much completely disappeared for a long time. Then mottled cropped up (at Garfield, I think). People went overboard at the novelty of the mottled to the extent of nearly losing the black (my take on it).
So, I think they are the same breed.
Bringing in mottled isn't an ideal solution. But I looked pretty hard for black three or four years ago and the best I found were the references to Garfield. There may be some (I didn't find you, either) but I don't know how to find them. Maybe lots of asking on social media.
There are pros and cons to the black being dominant to the mottled. You'll get more mottled cropping up even many generations later but at least you will know when you have some black.