Have other countries, not just America join in on the Cuban embargo, so that there would be a worse "Special Period" that could lead to the downfall of the Cuban regime. A major factor why the embargo doesn't work in undermining Castro is that no one else cares...in fact other countries have explicitly taken measures to prevent the US from punishing their companies for doing business with Cuba, and have been willing to keep relations with them even under pro-US governments! This is especially the case with Helms-Burton, where the EU threatened to challenge the US at the WTO, and Canada passed the satirical "Godfrey-Milken" bill in retaliation.
Additionally, having other countries join in would make it harder for Cuba to switch their economy from selling sugar to fellow communist states to tourism (especially from Canada and Argentina), which is OTL their major basis for their economy like with other Caribbean states (In fact, Cuba isn't that bad-off by Caribbean country standards in terms of living standards, but from my experience is reminiscent of post-Mao, but pre-reform China, so still fairly poor...).