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?