I ended up using nginx: http://nginx.org/en/docs/windows.html
I added the following to my conf/nginx.conf:
location /site1/ {
proxy_pass http://localhost:8081/;
}
location /site2/ {
proxy_pass http://localhost:8080/;
}
And configured my two apps (site1 and site2) to run on ports 8081 and 8080 respectively. This effectively simulates the shared tomcat deployment (one domain/port) while using two running instances of tomcat embedded (on two ports).