I'd want to go perpendicular too, but make sure there's no bowing in the floor in the hallway. Have you put a level on it?

Because of how large your kitchen area is, I think you can do it either way. I tend to run my tiles/LVP in such a direction is to make the room look larger, rather than shorter and stubbier. I have been in a lot of houses with LVP, and I’ve never thought about the bowling alley comment. I actually could see that for your house given how long that expanse seems to be. Another fun thing to mix it up might be to have the bedrooms done at a slightly different orientation. Obviously, there would be a transitional piece at the doorways. You have lots of options, so be creative!