You don't want Max Ray Distance; you want ray Extrusion, and honestly, you probably don't even want that (I'll explain.)
Okay, first thing first, let's open your file, hide everything but your low and high, and disable "in front" on your low so we can actually see the relationship between these two meshes. We'll also disconnect your normal map input so that your bake won't be depending on what it's writing:
Your low is the red bits poking through. Where your white, high poly bits are in front of your red, low poly bits, your low won't see the high. So we need to expand the low poly. Let's use a displace modifier to see what happens when we use ray extrusion:
Displacing a model evenly along its normals is exactly the same thing as enabling ray extrusion, which is why I said we probably don't even need extrusion. I prefer displace modifiers because I can actually see what's happening with that, rather than just guessing at ray extrusion distances.
What we can see is that there is no number that will give us sufficient ray extrusion without also causing self intersection in the low poly, which isn't what we want. This is not a model that we can do with ray extrusion alone; if we want to bake a high-to-low normal map on this, we need to use at the very minimum a cage, and we may need to part it out into individual bake bits, to be composited together in an image editing app.
If we use your other low poly, disable in-front display on it, and disable its subdiv modifier, it will work a little bit better. We'll still need a cage, but making a cage is pretty easy: duplicate the low, select bits that are still inside the high poly, and alt-s them out:
I'm going to leave making the cage to you, however.