What is being measured in the two slit experiment does exist. If it did not there would be nothing to measure. But its character as a wave or particle depends on how you measure it-with one slit or two.
This is exactly how Kant described things in themselves-they exist but their existence is unconditioned reality. Their character is however half dependent on them and half dependent on the mind
These two levels of reality are helpful for me in my religious point of view based on the Old Testament (the Oral and Written Law). Often, I have to say some statement in the Old Testament is referring to this hidden level of reality, --not the phenomenal world. That is this world is conditioned reality while the hidden world is unconditioned reality.
I have on my own understood the Old Testament along these lines for years but did not write about it.
That is what you measure in Quantum Mechanics is expectation values just like you do when learning Probability Theory. That is the bracket notation in Quantum Mechanics is exactly the same thing as the expectation value in Probability. The ket vector is the original state and the bra vector is the final state and the observable is in the middle.
But don't talk to philosophers about any of this. They don't understand this stuff at all and either ignore it and think it is not relevant for metaphysics which they deny exists. Or they get it wrong.
[In plain English you have to have with QM either independent reality or locality. Since we know Locality because of Relativity therefore independent reality has to be thrown out. Simple as pie.]See this talk by Murray Gell-Mann