Based on what I read, I would recommend that Dr. H seek a career outside academia. I'd advise Dr. H to seek out, via friends and acquaintances, other math Ph.D.'s who have successfully found careers that they are happy with and learn about their jobs, as well as how they managed to get them. There are not a few companies who have found math Ph.D.'s worth hiring, but you do want to walk into the interview sounding knowledgeable and motivated (i.e. with a positive and confident attitude), even if you don't have much experience. So you might want to devote some time to learning some additional stuff either on your own or in courses. Finance is a popular choice, but there are many others available.

Of course, if Dr. H really, really wants to do academic research and teaching, then I'd advise the greatest possible flexibility in terms of the location, quality, and type of academic institution.