Final answer:
The family utilized various transportation methods, including old family carriages, a sloop, a transport ship, and later, a limousine to leave the city.
Step-by-step explanation:
From the provided excerpts, it can be inferred that the family took different modes of transportation when they left the city. They used old family carriages and carts as they followed the rear of an army column, and later on, they transitioned onto a sloop and then a transport ship that brought them to Saint John. The mention of an old junk which served as a station wagon suggests an old, possibly rundown vehicle at one point, whereas in another excerpt, a limousine is used to avoid showing an automobile to others. These variable experiences reflect the diverse realities faced by Loyalists in New York or as transplants to Canada during the relevant historical period, especially in the context of transportation and moving.