Can't help with a recommendation for a navy but for a darker blue-gray take a look at BM Deep Silver or BM Brewster Gray.

It's not as dark as navy, but we have BM Van Courtland Blue in several rooms and love it.

BM Hale Navy is beautiful, but I don't see "slate" in it. SW's Steely Gray is a nice medium/dark blue-gray. Its on-line photos don't show its real-life appearance accurately at all though IMO.

I used Ellen Kennon's "Dave's Dream" for our powder room. It is a very dark slate blue with no purple undertones. You may be able to see that it is actually the blue of the veins in our slate floor. It is a stunning, rich color but unfortunately does not reproduce well in my photos.

Another vote for Hale Navy. It's very dark but very beautiful!

Oh the Van Courtland Blue and the Brewster Grey look gorgeous! I will have to pick up some chips.

sis3 I am not familiar with that brand it looks nice in your pictures (dark paints are hard to photograph I know) where did you get it? I googled and could not find it.

We close on our new place in 10 days but won't be able to move in until June, so planning ahead for the decorating!

Ellen Kennon has a range of gorgeous Full Spectrum Paint colors. Full Spectrum and Ellen Kennon have been discussed on this site many times. A search may turn up some helpful threads.

If you are not familiar with FSPs they are fabulous colors produced without using black. The effects can be absolutely stunning! If you are wanting to create something special I urge you to check out FSPs and also take a look at the photos on Ellen's website. EK's colors are made with ICI paints. Ellen sends the formula for your chosen color to your local ICI dealer to mix for you to pick up. Mine is always ready within an hour or so of placing the order!
I am linking Ellen's website below.

Here is a link that might be useful: Ellen Kennon's Full Spectrum Paints

Here, from BM America's Colors, is a Charlotte Slate accent wall next to Nantucket Fog from the same strip on the deck.

It was plenty dark enough for me, given the strong colors of my fabrics and the size of my rooms, but I can see how will tall ceilings and neutral upholstery you might want something darker. I had never had blue walls before, and I liked the color a lot.

I checked out those greys but they are not blue enough for what I had in mind - though pretty. I think Vermont Slate and the Charlotte Slate posted above are more in line with what I imagined, but the monitor can lie so i have to go to the store and look at the chips!

I don't mind dark for our bedroom which is what this is for. The living area will be neutral to keep it from looking dark. We will not have tall ceilings, we're moving out of our loft condo into a townhouse with rather average-low ceilings (I think they just feel low after living in a loft). But the bedrooms have big windows and I prefer a darker bedroom anyway.