Is it permissible to resign from a university job that is not performed in a way that pleases Allah, given the availability of an alternative private job, and will the one who resigns be rewarded for that, and does the social prestige of the position preclude resignation?

A Muslim is required to stay away from whatever displeases Allah, for Allah created His servants to worship Him. If you cannot perform your work in a way that pleases Allah, and you fear falling into disobedience, then it is your duty to leave it, seeking Allah's pleasure, especially if you have a private business that suffices you. Whoever gives up something for the sake of Allah, Allah will compensate him with something better. There is no benefit in social positions in exchange for Allah's displeasure. In summary, it is your duty to leave the work, and for that, you will have a reward from Allah.