It doesn't even have to be restraining in the sense of direct regulation that is clearly for that purpose. Even changing the wider political structure can have a positive effect on the direction in which political and economic progress flows. For example, parliamentary political systems can shape the nature of political discourse and have such an impact on how politics functions that they become less susceptible to devolving into authoritarian regimes. Obviously this isn't an example related to constraining capital, but you get the idea of how the simple structure of an institution can reduce or enhance the likelihood of a certain sequence of events.
Depends on the conservative party. It's certainly interesting to note that informal institutions (i.e. cultural norms and whatnot) can have an effect on the kind of issues each party will come to advocate irrespective of global similarities. Some 'conservative' parties are far more accommodating of environmental problems than others for that exact reason. They may decry excessive regulation, but it's about hitting that magic balance.
And whilst this is certainly an issue, I'm yet to be convinced that completely transforming the global socioeconomic system is the most viable, politically feasible and desirable solution.
As for ecosocialist theories, cheers for the link, I've actually been looking for decent works on it from an empirical standpoint, but I've come up with little.