One of the most critical aspects of strategy when trying to create change in politics is having a comprehensive plan. You need to understand the realities and possibilities of politics and not allow ideological purism from limiting what you can accomplish. Mainline political parties are large and heterogeneous groups. Depending on the way that issues are aligned between your national duopoly you are going to find people you can work with from both parties.
You probably align more closely with 1 but its not 100%. Certain groups in American politics refuse to accept that even one party has politicians they can work with. This makes no sense because in a truly open multi party system most parties understand the need for a coalition. Most successful positive policies have been passed into the mainstream this way. The Green Party in Germany and their work with the Social Democratic Party is an outstanding example.
Working side by side with politicians that lean your way inside mainline parties is critical. Its also critical to pair this work with having your own party create incentives and pressures on mainline politicians to campaign for your positions. Non-party pressure groups as well as third parties waiting to welcome voters frustrated with mainline parties are both powerful ways to shape mainline party policy in a favorable way. Finally you need an inside strategy. Influencing voters to support your ideas causes the politicians that represent them inside mainline parties to change their stances. Both direct pressure on politicians and indirect pressure from their constituents are important. Your approach is three-fold. Outside, Inside, Side By Side.