Do angels have an immortal soul like humans, but simply don’t incarnate like humans and suffer the experience of “starting over” as helpless infants with no memory of their true origin and past experience?

This is very much the case. They have an immortal soul and they were created and have persisted over a vast span of time. In this respect, they are like human old souls, but have the benefit of an awareness of all that has happened through their vast history and are not moving in between planes where they are, at times, at a level where they cannot recall their origin or their past experience base, as happens with humans when they incarnate as physical beings. This creates huge disadvantages for the human being but is not true for the angelics, who have accumulated tremendous knowledge and skill in interacting with all kinds of life-forms, as well as the other forms of consciousness involving the physical aspects of earth environment and other worlds. They are adept in many ways with many duties and are a tremendous resource and assistance to Creator because of their skill and sophistication. They can be relied on to implement divine principles without fail and to minister to all in need. They still must obey the rules of engagement to not bail out humans who create problems for themselves without due consideration for their free will right to cause problems and even destroy themselves. But when there is any outreach to the Divine, angels are often the instrument answering the call—to right the wrongs, to rebalance things, to bring healing and assistance of all kinds, depending on what is taking place and what might be needed to preserve life or restore balance. They are the best friend of divine human because their very existence was intended to be an aid and a source of divine help for all life forms and especially for the human beings with the extra challenges they have.