As much as I hate to say it, I think learning to make use of the same communication strategies that bad-faith argument people tend to use is the way to go. In specific:

1. You're not trying to "win" against the person you're talking to. That is, in a lot of cases, impossible. You're trying to communicate your message to an audience (which, sure, includes the person you're talking to). You're not limited to the framework the person is trying to give you. You can just say your message.
2. Short, tangible talking points can be more effective than detailed and accurate explanations. Pick one thing that's true that encapsulates a little example that's hard to deny about the way you're saying the world is, and stick to it. This technique is so effective that it can create a narrative even if the overall world-picture it creates isn't actually accurate; if the narrative you're trying to construct actually matches with reality, then you'll have a broader base of little exemplar anecdotes to draw from.
3. Stay patient, don't get irritated, don't feel like you have to "respond" to everything. If the other person's talking in good faith and asks a relevant question, then sure, you should answer it. But if they're just doing a Gish Gallop or something, it may be more effective to call out the Gish Gallop and keep explaining your own POV than to try to debunk every single thing, or to get them to "agree" or pin them down to something they're saying that's wrong, when they're not interested in cooperating and the effort will just derail you from making your own side of the argument.