I'm in a slightly strange situation. I have been playing the piano ever since I was a kid, and have in recent years taken an interest in drumming. Not having consistent access to a real drum kit, I got into the habit of performing rhythmic passages using alternative means (my desk, my body, the car's steering wheel, etc.). This has gone on for several years, and when I finally sat down next to a real drum kit, I was pleasantly surprised to find my practicing translates well to a real kit, and I can perform and maintain fairly non-trivial rhythms on it.
The problem is that for some reason, it seems I self-trained unknowingly as a left-handed drummer, even though I'm normally right handed. That is, even though my dominant hand is my right hand, when I play a regular (right-handed) drum kit I find it significantly easier to use a left-handed hands assignment, i.e. when playing a basic rock beat, I uncross my arms, hitting the snare with my right hand and the hi-hat with my left; hitting the ride requires crossing them again which is slightly awkward. Additionally, since the pedals cannot be exchanged in the same manner, I end up doing essentially left-handed but right-footed (?) drumming: right and left feet do bass and hi-hat respectively, while right and left hands do snare and hi-hat (instead of the other way around).
When I try to play the kit "correctly", it feels like taking quite a few steps back and I can't do half of what I can easily achieve when my hands are switched.
Now that I have somewhat more regular access to a (right handed) drum kit, I need to make a decision: I can either continue to play and practice as a left-handed-right-footed drummer, building on the foundation of what I've already trained for; or I can try to unlearn everything and start from scratch as a normal right-handed drummer.
So, my question to drummers and drum teachers: is it even possible to unlearn something like this? Would using this strange layout limit my progress in the future? Conversely, would I gain anything from switching now, despite the price of retraining my hands to do the opposite of what they're used to?