Dilemma of the Catholic academic job search

What's a newly-minted-Ph.D.-packin' orthodox Catholic graduate to do? Here the problem as posed by one recent doctorate looking at Catholic English departments in "Catholic Colleges and Orthodoxy" (Words, Words, March 12, 2009):

I'm starting to think that I have no business applying to Catholic colleges, since one of my concerns is orthodoxy--actual adherence to the Church's teaching, broadly conceived. What kind of battles will I be in for if I go to a school that violates or disregards Church teaching on life issues, ordination of women, and even questions whether it is just to exclude non-Catholics from the Eucharist? Matters of conscience even get tricky at a secular, state school; how much more so if the administration of a Catholic college where I worked were to promote an agenda opposed to Church teaching? And yet, I interview by phone tomorrow with a college that was founded by an order that ABSOLUTELY supports women's ordination. Campus ministry reluctantly acts according to the will of the local bishop in refusing Communion to non-Catholics (not the Vatican, you will notice). I even emailed for clarification on this point, and the tone was one of remorse and sad disagreement. I have no idea how this would influence the tenor of the English department, except that the faculty members list the subjects about which they will willingly be interviewed by the press on their web pages--yes, that's ENGLISH faculty, people. Yet they're hiring for a position that would, essentially, oversee the school's orthodoxy, including screening new hires for willingness to adhere to the school's mission, uphold Catholic identity, etc. This person does not have to be a practicing Catholic.

What to do??

[Hat tip to R.B.]