[SalesForce] Cannot get slds-col to stretch if they are embedded in child slds-grid

I'm creating a custom theme layout. I am stuck on getting a basic layout created.

Here's how I want the layout to appear:

Row 1: Logo (align left), Profile (align right)
Row 2: Menu
Row 3: Body Contents

Wrapping all rows, I want a centered, large container, so the webpage max width is 1024px, but it is centered on the screen.

So to created Row 1, I came up with something like this:

<div class="slds-grid slds-grid--align-center">
    <div class="slds-container--large">
        <div class="slds-grid">
            <div class="slds-col">
                <div class="slds-box slds-box--small slds-theme--shade slds-text-align--center">Insert Logo Here</div>
            </div>
            <div class="slds-col">
                <div class="slds-box slds-box--small slds-theme--shade slds-text-align--center">Insert Profile Here</div>
            </div>
        </div>    
    </div> 
</div>

Text is centered, but the columns do not stretch. They take up just enough space to display the text.

If I take the inner grid and display that, they stretch just fine:

<div class="slds-grid">
    <div class="slds-col">
        <div class="slds-box slds-box--small slds-theme--shade slds-text-align--center">Insert Logo Here</div>
    </div>
    <div class="slds-col">
        <div class="slds-box slds-box--small slds-theme--shade slds-text-align--center">Insert Profile Here</div>
    </div>
</div>  

But if this snippet is inside a container, it stops stretching.

I tried dozens of alterations, including using a fluid container inside the large container, using width=100%, but nothing has given the desired effect.

How can I force the grid/cols to stretch to fill its container?