Instead of using JAVA_OPTS try to set the variable as java_opts. I know it seems strange but this should actually resolve the issue and get Heroku, Play and New Relic to be nice to one another.
You also want to modify your Procfile adding the following:
web: target/universal/stage/bin/YOUR_APP_NAME -Dhttp.port=${PORT} -J-javaagent:/app/newrelic/newrelic.jar -J-Dnewrelic.config.file=conf/newrelic.yml
Cheers Adrienne (TSE at New Relic. Inc)