I started off boxing as an orthodox despite being left handed, I did it for quite a while, and when I switched over to muay thai I did it again for a while.
In the end I was persuaded by an expertboxing.com article to switch to southpaw and it's worked out well. I can switch hit quite well now, tending to go on the offence more from orthodox and countering more from southpaw.
The main reason I switched however was because I was too one handed as a fighter. I would throw jabs and lead hooks but except for finishing combos with a right hand, I just didn't use it enough, which is why I switched, putting my power hand in the back made me a lot more versatile and helped me develop a wider variety of punches.
So unless you're absolutely dedicated to throwing that rear, weaker hand as much as possible in bag drills and sparring sessions to make sure you use it, then you should go to your natural stance for the sake of the accuracy. Often there isn't much difference in power between a right and left hand (I wouldn't be able to tell you what I punch harder from) but its that accuracy that matters more.
So yeah, either work your weak hand a lot more, or switch to orthodox.