Probably any of the Connection pools can be configured to deal with this in any number of ways. Ultimately, all that REQUIRES_NEW is probably forcing your app to acquire more than one Connection per client, which is multiplying the stressfulness of your stress tests. If pools are hanging, it's probably because they are running out of Connections. If you set a sufficiently large pool size, you might resolve the issue. Alternatively, as Arjan suggests above, you can configure pools to "fail fast" instead of hanging indefinitely, if clients have to wait for a Connection. With c3p0, the config param for that would be checkoutTimeout.
Without more information about exactly what's going on when you say a Connection pool "stucks", this is necessarily guesswork. But under very high concurrent load, with any Connection pool, you'll either need to make lots of resources available (high maxPoolSize + numHelperThreads in c3p0), kick out excess clients (checkoutTimeout), or let clients just endure long (but finite!) wait times.