Righties on the right, lefties on the left is a conventional wisdom teach to me. You need to understand the trade-offs.
First, imagine a line drawn from your current release point to the catcher's mitt. Then imagine a line drawn from your release point to the catcher's mitt if you started on the glove side of the rubber. Assume for discussion sake that those two release points would be 10" apart at the rubber and would converge to the same point in the catcher's mitt. Now imagine how close those two lines would be where they pass through the strike zone. Obviously, they will be fairly close together - close enough, in my opinion, to not make that big of a difference to a batter (unless maybe if you stride way offline from the target and come back using the crossfire).
Now consider that your shoulders want to square up to the target and that striding away from the centerline of the rubber means they have a "bigger corner to turn" to get squared up. The question is can you accomodate this without doing something else that is detrimental to your delivery? A common thing to happen is for pitchers to shift their posture to the glove side to help get squared up. A late posture change will usually pull the release point back and raise it up. If your trying to throw a breaking pitch down and in to a RH batter, this will make it harder to get the pitch down and it will likely reduce movement. Extra effort may be needed. And later in a game as you start to fatigue, it will become even more difficult to remain consistent.
So, the trade-offs are the possible benefits from the slightly "better" angles vs. the possible issues associated with getting aligned with the target. I hope this info will help you be more self-aware and better evaluate what's best for you.