11.7cm or 11.2cm Breast Implants for a 13cm BWD?

Since you are having a periareolar lift, there should be some caution and concern about using a implant that may be too large or too heavy...that form of lift does not support large implants well.
So the voulme of your implant (in cc's) may limit your implant width choices. If you want as much cleavage as possible, then an implant that is slightly over your BWD may be OK. On the other hand, the perioareolar techniques tend to flatten or truncate the breast some, so a higher profile, narrower implant may be required.
As long as your doc knows your aesthetic desires, and you know the possible limitations, you should get te results you want.

I am sorry to say this here but it is not your final responsibility to choose the right. This is what you board certified plastic surgeon needs to do. You job is to describe and convey to your surgeon the look you are going for and what you would like to achieve, even the ballpark of size wise what you desire.
But the ultimate decision needs to be in the hands of your plastic surgeon as he or she has a lot more knowledge and experience as to what would work better for your body.

I would not get any smaller than 11 cm but this would depend on your skin pinch, the distribution of your mammary parenchyma and the width of your cleavage and breast separation. Going any smaller could make your breasts appear more separated or inadequately fill your skin envelope.