What are your thoughts on my thoughts of quantum entanglement and forces acting on the photons via extra dimensions?
No, quantum entanglement can not be accounted for classical forces acting in other dimensions.
Any multi-dimension theory would give you just another hidden-variables theory. There are no hidden-variables theories that can explain quantum mechanics and are at the same time local, realistic, consistent with relativity, and gave the Riemann-like topology of space.
An example of a hidden-variable theory is the Bohmian interpretation, but it explicitly violates relativity (superluminal motion).
Postulating higher dimensions will just give you a hidden variable theory.
Special note about the string theory. It is not a theory that tries to explain quantum mechanics in terms of classical mechanics. It tries to explain fundamental interactions and particle physics. The strings are already quantum by design. It is not like "vibrating classical strings yield quantum mechanics".
There were attempts to derive quantum mechanics from classical mechanics by postulating nonstandard
topology. I.e. we not only have additional dimensions, but also they are non-Riemanian. A simple example might be a space with lots of tiny wormholes - one could call it "foam space". Important: it's
classical foam, not quantum foam. The inherent randomness built into the space would give us apparent randomness of the quantum mechanics.
Another attempt I heard of was a "string concept" (not the same strings as in the string theory) that two entangled particles are connected with a string in a higher dimension. The problem with that approach is that it gives you superluminal communication, not the entanglement.
The problem with quantum mechanics is that it doesn't really postulate sumerluminal information exchange. It postulates
correlation of distant events, which is not the same. All classical theories either give you too little (no FTL information exchange, no correlations) or too much (correlations, but also FTL information transfer).
One explanation might be that quantum mechanics simply can not be derived from any classical theory, FTL or not, no matter how many dimensions and what topology.