Wouldn't use Digital Ocean for shit, there are multiple stories of users were they cancelled accounts (actual production systems) because of sustained use or bogus DMCA claims.
Otherwise it's a way to convenient method to cripple the competition or shut someone's personal website down for shits and giggles.
Do you colo, or use non-US based providers?
The EU notice&takedown procedure does not entail that you loose protection for simply forwarding such notices, all that matters if someone responsible is actually reading the contents. If I don't give a shit about the notice then you can send a C&D and if I still don't give a shit, you can sue me. Or you make someone at my provider somehow care.