First, no one contributes significantly to the climate fund (and it probably wont be until theres significant damage from climate change). The goal was $100b.. the US has pledged $3b, and EU countries have pledged $4.7B.
2nd, it is not outside of US political control. Countries do not pay all of their pledges into the fund. They make payments, basically as needed. The projects that are funded are public. If the US does not like the projects, the President can just refuse to contribute anything else to the fund. I imagine, the US could just earmark funds too (what are they going to do? refuse money? doubt it.) If that's not good enough, the US can always just contribute nothing.
Paris was signed by so many countries because it is completely symbolic. There's no enforcement of anything, and any pledge or goal is entirely up to the country.
Your plan sounds like a good idea.. put an estimate of the amount of carbon that reduces... and you've just created a goal to reduce carbon (just like in Paris!).
In Paris, what happens if your idea turns out to be ineffective? Nothing. What happens if you change your mind? Nothing. What happens if you want to do it differently? Nothing.
That's literally what a carbon goal in Paris is... a vague non-specific plan with a carbon estimate.. that you can change later.
Because Paris forces nothing on to anyone.. the question it really answers is, do politicians/reps of the countries believe in climate change?
Trump has said he believes it's a fraud, completely made up. That's why he withdrew. He has fired climate change scientists, and demanded agencies no longer research the climate, and has removed funds from those agencies for climate change. He has left the heads of scientific agencies completely vacant (no nominations). He doesn't have a plan to accomplish it some other way -- he plans to do nothing. If there was a plan, he could just make that our new paris goal.