Is it possible to truly bend time through a request to the divine? Does this take any special belief in order to happen, and how much extra time could someone gain, for example, to complete a project with a looming deadline?

It is perfectly possible to bend time in order to increase productivity. This can be done to allow a person to do a body of work seemingly in less time than would ordinarily be required because, in effect, you are stopping time to allow this to happen. What is actually taking place is a time dilation that acts as a kind of looping locally for the individual, and the individual alone, and those things involved in his direct physical experience and environment. So this will not affect the larger world but can be very useful and a great benefit when there are serious tasks to perform and time is limited. A person can gain typically an hour of time quite readily in this way and, in certain conditions, significantly more if there is a great need to do so. This will require sufficient belief as it is one of the things people will tend to have too much native skepticism to do effectively at first but, like anything, belief can be cultivated and particularly though practice, grow to allow such experiences. You yourself have done this successfully in the past and can do so again.