I noticed that headers use bold which makes the use of <strong> in headers invisible. Changing the style of <strong> (and <b>) to "bolder" might be appropriate.
Perhaps there is a reason that increasing font weight in headers is undesirable, but I am guessing that the issue has not arisen because headers are rare and adding strong emphasis is rare (and the two might even be negatively correlated).
For an example of where "bolder" is not unreasonable, see the "Sometimes strong emphasis (bold) is appropriate." header in this post.