When I place a TextBlock inside of a Horizontally Aligned StackPanel it does not wrap. I realize that this is because the available width of the StackPanel is PositiveInfini
It's because you're using Horizontal orientation on the StackPanel. That means that the StackPanel is giving full width to each child control, and then laying them out horizontally - even if that means exceeding its bounded/visible width. Because there's nothing to constrain the width of the TextBlock, it doesn't wrap.
If you switch to Vertical orientation then the wrapping works, but I'm guessing there's a reason for you specifying otherwise. Can you show what layout you're trying to achieve?