dspace-rest uses old versions of Jersey artifacts, including one for Spring 3 while we now (in DSpace 7) use Spring 4. One problem with this is that Jersey is dependent on org.glassfish.hk2.external:bean-validator, which incorporates in its own JAR classes from an old version of JBoss logging. Hibernate depends on a newer version of JBoss logging. As a result, I've had V7 bin/dspace crash as soon as it tries to open the database unless I delete bean-validator.jar from lib/. It's possible that in addition dspace-rest would fail to start, but I haven't tested that.
I suggest moving up from jersey-*:2.22.1 to :2.26 and particularly from jersey-spring3 to jersey-spring4. After building with these changes, I no longer find bean-validator JARs anywhere in the installer directories, which should eliminate the crashes I've seen.