The Many-Worlds interpretation of quantum mechanics is consistent with local realism.

What would happen if a particle measurement had a probability with irrational numbers (in every base)? What would the outcome be?

And I feel that MW would need a pilot wave that carries the information for every parallel possible outcome for entanglement to work, wherein certain pilot waves cause universe splits starting from the point where they overlap and others merge - if you measure the spin of two entangled particles you get two waves that meet where X+X and Y+Y don't interact, but X+Y and Y+X does and thus create new universes. I don't see how the wave-less versions hold up when there for example are orientation-dependent probability and a ton of other crap like that. What else makes the particles interact with exactly the right universe?

Edit: Not to mention how complex MW would have to be to explain the delayed quantum eraser experiment.

You're thoroughly confused about what MW is.

In what way? There's no one canonical MW either way, my version with growing parallel universe bubbles that merge or split is just my interpretation, as the other versions I've seen seem to be unable to address various issues

There is a canonical MW interpretation. The MW hypothesis is just that reality is the evolution of the Schrodinger PDE on a configuration space with no other modification such as pilot waves or collapse required. The math is really quite simple (this simplest of any QM interpretation). It doesn't have parallel universes or bubbles as fundamental objects.

And by what mechanics does that happen? How do the universe "know" which particles should behave how in delayed eraser experiments, for example? It just... Happens? How are the particles "separated" and "merged" (in lack of better terms) in the configuration space?

Particles are not fundamental, either, and thinking in classical terms will yield only confusion. You'll find a good non-technical introduction to the MW interpretation here: http://lesswrong.com/lw/r5/the_quantum_physics_sequence/

My basic justification for my interpretation: either entanglement of two photons makes all of spacetime branch out into two instantaneously (however that's represented in the configuration space - Pluto wouldn't wait for the event to enter its light cone to now diverge into two "branches");

Or every point in the universe is essentially an independent configuration space, linked in a kind of matrix, in which the fact that the photon we sent to Pluto had spin X on measurement propagates outwards back to us and upon reaching us causes our configuration space to react accordingly in two different branches. After all the knowledge couldn't be available to you before it came back. Functionally equivalent to my bubble description above, only the terminology differs. Or is the configuration space infinite to the degree that all possible future outcomes is accounted for and represented in every point at once already, practically making it into a growing complex infinite web of interactions when following the time line forwards?

True, but it makes Occam spin in infinitely many graves.

I'm not sure why people believe this. I would address it here again, but better people than me have written on it: http://lesswrong.com/lw/q3/decoherence_is_simple/.