The crucial issue is whether you need to suppose the actual existence of parallel worlds (or parallel "parts-of-world") in order to explain experiment.

According to timeless physics, the past and future are just other parallel worlds. They might not actually exist, but since we can't really do anything unless they do, we might as well assume they exist.

Even without that, Assuming that a specific path through the waveform happens is pretty silly. All of it is vital to figuring out what happens, so why assume on piece of the past exists? If I were going to assume that it was mostly just reality conforming to a random point in a waveform, I'd expect it's one random point. Why would it be a path of them?

Bohmian mechanics

From what I can gather about that, it still assumes a waveform. In order for it to make the same predictions as quantum mechanics, which have been very thoroughly tested, it would have to have waveforms of huge numbers of dimensions. It would either have to have laws about how the waveform gets entangled, like the Copenhagen interpretation, or it would have to have the waveform include the position of every particle. In short, it assumes some other interpretation of quantum mechanics, and then adds particles on top of that.

Am I misunderstanding it?

One possibility I have considered is that the waveform is made of a huge number of interacting particles.

Oxford school's position

I don't actually know what that position is. My position is that the entire waveform exists. I don't know why the Born probabilities are what they are, but I wouldn't know no matter what they were.

it makes sense to say that there is no right definition of "blob", but it does not make sense to say that there is no right definition of "world", because the existence of the blob depends on the definition, but the existence of the world does not.

You're reading too much into that word. The terminology is a bit misleading. It's like a blob, not what you think of when you think "world".

I'd say the world, in the sense of what actually happens, is the entire configuration space. I don't know what makes us "experience" a piece of it, but it's as much a question of neurons as it is of amplitudes.