I figured out the problem. After reading http://community.jaspersoft.com/documentation/jasperreports-server-administration-guide/v550/jasperreport-structure and knowing that what I am trying to do is definitely possible, I looked closer into my main report, and saw that for the subreport element I needed to pass a data connection along to the subreport. I set Connection Type to "Use a connection expression" and se tthe connection expression to $P{REPORT_CONNECTION}.
