Just as a quick update, I messaged the CSA generic inbox and it wasn't a problem swapping the numbers/accounts. The concern seemed to be to ensure I was the same person across both accounts so they asked several verification questions. I had the same VISA paying on both, the only quirk I had was that they used my middle name on one account and my first name on the other, but since you can update that yourself under your online profile, it wasn't an issue. I also provided a copy of my driver's license showing both my names on there as well as the security codes they texted each line.
For anyone curious (since there were several users pitching "alternative" solutions that seemed to misunderstand my necessity of swapping accounts), my two accounts were 1 personal and 1 business. My long-standing number was on my personal account (phone number) that contained many rewards but I needed to swap that for my business account (phone number). If your number is ever ported, it terminates your account, and with that would go all your rewards, which is why it was important to ensure my long-standing account would remain with the number that stays at PM.
Maybe I got lucky as many others seemed to report not being able to do so. In the end, I'm not sure I would understand what the conflict is all about since if both accounts are controlled by the same person, there's no real conflict of interest. Plus it helps ensure you stay with PM. Perhaps what presents a challenge is swapping plans? I wasn't worried about losing an out-of-market plan. My priority was maintaining my rewards and my number, that was all, so maybe it's a different situation if someone is trying to hang on to a plan.
