"In Everett-type many-worlds theories ... you have to be able to believe that bouncing a photon off an atom creates new universes..."
Not necessarily. You could trying taking a five dimensional view of the situation. We know from relativity that time is a fourth dimension as real as the space dimensions and connected up with them into a four dimensional whole. This refutes the view that only the present moment is real with the past vanishing into non-existence and the future not yet formed. In the relativistic view, all moments in time, past, present and future are equally real and it is an illusion that only the present is real. We can extend this idea to include a fifth dimension of alternative possibilities. They are not suddenly and mysteriously created. They have "always" existed.

With respect to quantum randomness, that can be interpreted in the context of my previous comment presenting a five dimensional view of the Many Worlds idea.
Think of reality as a solid five dimensional block of space-time plus a possibility dimension hosting the many worlds alternatives. Discrete observable events can be viewed as tiny particle-like dots embedded in this greater reality. Some of these can be linked by directed lines, from past to future, in the time dimension which represent causality. From the dot in the past we could draw many such lines fanning out through the fifth dimension to the alternative causality linked results. Lines might also be drawn sideways in the time dimension representing not causality but quantum entanglement, suggesting an underlying unity between causality and entanglement. Perhaps some other dots could exist without causal links into the past. These are events that are simply there. They happened for no particular reason. They still have to conform to fundamental physical principles, especially the conservation laws, but they are otherwise random. If such dots exist, then there is fundamental randomness but if not then not. The Many Worlds interpretation is, in this five dimensional view, agnostic on the question.

Whenever quantum mechanics threatens to overwhelm me, I think of the philosophical quagmire surrounding the physical interpretation of the mathematical results and thank my lucky stars it's not examinable :)

I do believe most probably the select few who's opinion on QM that are being taken seriously. Simply have already put to many limits on what they deem accurate or inaccurate. For Example: Who's to say super position exactly has any true real science to the principles of QM....? Like seriously the understanding of QM can not be defined with such theory or experiments of a cat being dead and alive, or multiple beings of the same body in different dimensions. If one has yet to realize, QM is for certain much more simplified than all previous works of science. It's the Salt & Pepper. Not the Cake.
Using simple logic as QM or QM thinking.. When I listen to these guys say there's a cat dead and alive etc etc... My Quantum instinct says, Super Position in QM is more like the ability to recycle a plastic bottle into a Plastic Plate... The possibilities for the plastic bottle to make up any and every other object that is defined of its unique atomic property's is Infinite. So to say in the ideas of QM... If I have a Plastic Bottle.. I also have a Plastic Plate, Pen, Clip or anything else that is formed out of the same nature in which my plastic Bottle is..
QM truly defines such principles that one with a value of energy can become any and all property's of mass in the universe with the right ingredients of Energy.

@Adam_Smith. Agree with your extra-dimensional interpretation in parameter space, but we ought to look at CONVERGENCE of events in 5-space as well as an annealing of the quantum phenomena that cause divergence. As larger quantum objects, the experimenters and their apparatus are possibly subject to interactions that cause the diverging Everett worlds to come together again, so we do not experience superposed states on the macro level. I propose no mechanism for this. Julian Barbour's work has great bearing on this issue. He sees a "probability fog" spread along the parameter points denoting the higher probabilities of some positions over others. The tiny quantum splits just vanish leaving us a perceptible and stable timeline.

Lucky for us we didn't need to invent matter & this all was provided to us for our enjoyment. Because of humanities backward engineering of everything. I will keep to this perspective and respectively read this piece backwards.

waves or particles- fluid dynamics? where is the transition from laminar to turbulent with neutrinos?
The bending of space near gravitational bodies is only detectable if you are outside the effected space and then does your mass affect/effect the measurements? If space is shorter(bent) relative to the assumed constant speed of light(so the math is solveable) -Is it still constant when it traverses a 'bent' path that appears linear to us?
Why would you limit God to physics? (paraphrased very loosely....)
tri-state analogies keep getting in the way- alive or dead? or? The proverbial cat for any variation on unified field theory would be where the density is such that the neutron,proton and electron are all one mass that doesn't have any motion at all- possibly why gamma ray burst emit from black holes as the mass is converted to energy(???)...

QM is such a horribly abused term.
It seems that every time I turn around that somebody is mis-using it to try to bring credibility to whatever pop foolishness that they are trying to pass off as "scientific".
Typical example: "Since Quantum Science has proven that anything is possible as long as there are an infinite number of variables and we KNOW that the Universe is infinite- therefore,somewhere there is a world where Dorothy still lives in Oz!"
Such people also use "reasoning" such as "Ancient Aliens had to exist- because if they didn't, then how did they build everything?"
As I watch science,history and politics devolve into un-reality TV shows, I am losing interest over straw-man arguments of all sorts.
I think far too much of that which is called "science" is really just "scientism" impersonating science.

At my age I love to try to understand things like QM, it chases the cobwebs out of the corner of my brain and replaces them with baffle. I am encouraged to find that real scientists have difficulties also.

The word "consensus" has no place in science.