Is it permissible to engage in anal intercourse with one's wife if she is unable to engage in vaginal intercourse due to health reasons, in order to avoid falling into sin, and does this fall under the principle of "choosing the lesser of two evils"?

What you have mentioned regarding your wife's condition does not permit you to commit what Allah the Almighty has forbidden. Therefore, you must repent for what you have done, for fornication is a heinous evil, and anal intercourse with a woman is among the gravest sins. Your wife must repent for complying with you in this, and both of you must cease this reprehensible act and strive to find a cure for your wife. If you are unable to do so or her treatment is not feasible, then you must marry a second wife to protect yourself from what is unlawful. If you do not have the capacity for that, or you are unable to manage two wives, and the situation would lead you to what you mentioned, then you are obliged to divorce your wife and marry someone else. If you are still unable, then you must fast.