What if I said we will have a Reverse, Natural Turn
Unlike many other dance terms, "natural" and "reverse" are mutually exclusive, because they mean exactly the opposite of one another... You can't be simoultaneously turning to the right and left. You
can often combine two concepts (for example, a hybrid Tumble Turn and Wing action is called a Tumbling Wing), but not when those two concepts are mutually exclusive.
Maybe we should have a Natural Double Reverse Spin
We can, but again your nomenclature is skewed: One cannot be turning to the right and left at the same time. Assuming you're talking about a Double Spin that turns to the right, the term you're looking for is "Double Natural Spin". It's a very common action in open (non-syllabus) competitions.
Or how about a Natural Reverse Spin Turn.
"Natural Reverse" is yet another oxymoron, so I think you mean to say "Reverse Spin Turn". Actually, there is such a thing, but it tends to go by a different name: Reverse Pivot.
Do it as you wish but give it a name of its own.
Whatever works for you is fine, but remember that the more you defy convention, the more you isolate yourself from the rest of the dance world. Most people do not try to invent a new name for every minor variation of the same step. A Natural Turn is a Natural Turn, whether the first step is taken in-line or outside partner. In fact, in the bronze ISTD manual, the name Reverse Turn is given to at least 4 different patterns in as many different dances. Totally different steps, same name.
Regards,
Jonathan