Who cares if there's no gravity? Gravity wasn't sent down to us from heaven on a stone tablet, it's just a concept that lets us make predictions. At school I was taught it was a force and at university I was taught it was a pseudoforce resulting from fixing a non-inertial frame. Both approaches give correct answers, even though they're conceptually very different. There's no objective way to say which is right; they're just different approaches to modelling.

And maybe the 4.7 is actually more correct? The 4-parameter model is an approximation that neglects friction and air resistance. Moreover the double pendulum is a chaotic system and chaotic systems sometimes have dynamics described by laws with non-integer exponents such as Lyapunov dimension. I'm just spitballing, but the point is that it's not a priori ridiculous.

It's definitely possible to estimate mass from images. How do you think we know the masses of asteroids and planets? No-one put them on a scale, we just record their motion and work out which value fits best.