Is it obligatory to resign from permanent employment in an interest-based banking institution upon finding temporary work in a non-profit institution, or to remain in the current job until permanent non-interest-based employment is found? And would immediate resignation be considered casting oneself and one's family into perdition?

If your work in the institution is not related to usury, then it is not forbidden for you to remain in it. However, it is common for work in such institutions to involve aiding usury. If the work is proven to be unlawful, then it is not permissible for you to remain in it unless there is an overwhelming necessity, and you must diligently search for another permissible job.

If the temporary work is renewable, you must leave it immediately due to the absence of an overwhelming necessity. However, if the work will cease completely and you have no other source of income, it is permissible for you to remain until you find an alternative.

Resigning is not throwing oneself into destruction unless you are certain or highly assume that this will happen, and your fear of not finding work might be merely an illusion. The principle is to adhere to strong resolve except in cases of extreme hardship that affect one's intellect or religion.