Megan — Thanks for asking this. I think it will take an entire new post to address this, that will come later. A couple of quick thoughts:

1. Yes, kind of tax on fossil fuel capital or fossil fuel wealth could help keep it in the ground.
2. Remember, you should not think about the Green Paradox (GP) in terms of average exploration and extraction (e&e) costs, but rather marginal e&e costs. For some important sources, e&e costs at the margin are already close to or below prices. See for example, this article about low profit margins of frackers: https://www.wsj.com/articles/frackers-scrounge-for-cash-as-wall-street-closes-doors-11559915320 .
3. Green policies that combine quantitative restraint of demand with a tax would reduce risk of GP, e.g., building efficiency standards. But beware of quantitative standards alone, such as CAFE standards for cars, which can produce a rebound effect.
4. The faster green policies (including taxes) are phased in the less GP. Worst would be no effective present tax or consumption restraint but a credible threat that such policies would be imposed in the medium future as the harm from climate change becomes more obvious.

Thanks again for asking.