A. Your roadblock may not be as frustrating as you fear, although you’re correct that official passenger records weren’t kept before 1820. A number of other resources might help, such as Genealogical Publishing Co.’s Colonists from Scotland: Emigration to North America, 1707-1783 by Ian Charles Cargill Graham (originally published by Cornell University Press in 1956). You can search this book on the subscription website World Vital Records.
Check WorldCat.org to find a nearby library that holds this volume, along with other potentially useful titles. Scottish Emigration to Colonial America, 1607-1785 by David Dobson, for example, might help you understand your ancestor’s passage to America.
Subscription site Ancestry.com has several databases for finding early arrivals from Scotland. Its Passenger and Immigration Lists Index, 1500s-1900s lists some 600 Scottish rebel prisoners transported to the American colonies in 1716. Among these, interestingly, is a James Dunlap, who potentially could be connected to your family.