> If you believe every outcome happens then one thing happening with higher probability than another loses meaning. The decision theory argument put forward by some many worlds proponents fails to solve this as it just provides a calculation you can do that produces the Born probabilities. It doesn't provide a convincing interpretation of them.

What further interpretation is needed? To the extent that we have a number we can measure, we have a calculation that can predict it. More interpretation would be nice, but fundamentally every interpretation of QM has this problem, it's not a unique problem with MWI.

> It assumes an infinite multiverse that is splitting into infinite variants in every infinitesimal instant, in possibly the grossest violation of conservation of momentum and energy (and therefore the corresponding symmetries) that could be imagined.

It assumes continuous unitary evolution that preserves momentum and energy in exactly the way you'd expect, exactly the way we already assume they work. Accepting that you can reasonably make calculations about infinitesimal changes is literally the foundation of physics, it's how Newton was able to make a theory of gravity (and people were just as unhappy about it then).