Thanks for any input.
Didn't see anyone offer this input, but if the exhaust from your reg is getting into your hood it means one thing and one thing only:
YOUR HOOD DOESN'T FIT RIGHT!
If your hood fits correctly it should form a nice seal around your face and there would be no way that reg exhaust could get inside it. Air, like water, follows the path of least resistance, and will simply go up and around your hood versus trying to work it's way under a properly fitting hood. This is especially true if you're wearing your mask strap OVER the hood.
I'm going to hazard a guess that your hood DOES fit properly and what is happening is that you are exhaling through your nose to some extent, that air is escaping your mask by slipping up under the skirt (which is likely tucked under your hood) on your forehead and around your temples, then finding it's way under and into the hood.
Wearing the mask strap under the hood won't help much, as the one thing it will do for sure is pull the hood away from your face where the strap goes under and then allowing reg exhaust (and cold water) to get under the hood.