EM and gravity waves don’t really interact like you suggest, but you could label gravitational lensing as a kind of emergent effect. High mass galactic or even stellar clusters can bend light (EM waves) from behind them, such that an observer could see objects not normally visible.
If EM did interact directly with gravity as you’d like, we would know a lot more about dark matter.
I am firmly one of those who doesn’t have high hopes for Dark Matter - or isotropic Dark Energy. For now I think MOND is developing a better representation of gravity and aspects of our cosmology. What I’m most curious about is what, if any, emergent/quasi-fields might form in space where it’s dominated by EM fields; I added gravity as it can still be a factor, given it is a omnipresent field throughout our universe - even in cosmic voids.