Actually I can think of about a half-dozen different common versions of a Hover Cross. Most are variations on entry/exit. For example, it's very common to omit the heel turn and enter instead from an Open Natural (especially from PP), Pivots, Outside Spin, etc. Common exits are Reverse Pivots, Weaves, or simply exit in PP.
Variations on the position itself are fewer, but it's common to play with the shaping in one way or another. Some prefer having the lady's head open with more of a rotary "Hinge"-style shape, while others prefer the lady to stay closed, and lay it out into more of a linear Same-Foot Lunge shape (not the base, mind you, which is still taking the Hover Cross Position O.P. on left, up on toes).
There's also quite an assortment of "Hover Passes", which are variations of the Hover Cross where instead of checking and reversing your direction on step 4, you continue moving through the position in the same direction. There are two main varieties of Hover Pass: The Traveling Hover Pass, and the Circular Hover Pass.
These, of course, are all variations of natural turning Hover Crosses. The reverse would certainly be easy enough to do... Easier than the natural version, actually, because the cross position would entail using right-side O.P. position, which is a much easier position to achieve than left-side. I imagine it would take a pretty strong leader to pull it off without a flaw on a social dance floor, however, because your average follower would probably be expecting a Closed Telemark.
Also, I wouldn't do the exact mirror image -- Instead of O.P. with your LF on step 6, it would be more sensible to take steps 5-6 as a Running Finish-type action, with the following forward step on the RF O.P. on right. Keep in mind that this leaves you moving D.W. against LOD, so be cautious about traffic, and flip it back around ASAP with some sort of natural action. Or better yet, check that RF step and back out into a Feather Finish (QQQQ).
Regards,
Jonathan